(Baylor Math Home Page)
The Baylor University analysis seminar meets on Wednesday afternoons from 3:30PM4:30PM in room 213 in the Sid Richardson Building. For questions about the analysis seminar or to be added to the seminar mailing list, please contact Paul Hagelstein, Andrei MartinezFinkelshtein, Tao Mei, or Brian Simanek (all email addresses can be found on the Baylor math department website).
3:30 PM SDRICH 213 
University of Cape Town 
Zeros of Laguerre Polynomials The sequence of Laguerre polynomials {L_{n}^{(α)}(x)}_{n=0}^{∞} is orthogonal on (0,∞) with respect to the weight function e^{x} x^{α} provided α > 1. The classical result that for each natural number n, the zeros of L_{n1}^{(α)}(x) interlace with the zeros of L_{n}^{(α)}(x) can (and has) been extended by several authors in various ways. In 2014, we proved that for each natural number n, the zeros of L_{n}^{(α)}(x) and L_{nk}^{(α+t)}(x) are interlacing for each t with 0 < t ≤ 2k and the tinterval 0 < t ≤ 2k is sharp in order for interlacing to hold for every k in {1,2,..., n1} and each natural number n. Recently, this was extended to zeros of Laguerre polynomials of equal degree, namely, for each natural number n, the zeros of L_{n}^{(α)}(x) and L_{n}^{(α+t)}(x) are interlacing for each t with 0 < t ≤ 2 and the t interval 0 < t ≤ 2 is sharp in order for interlacing to hold for every natural number n. For α in the parameter range 2 < α < 1, the polynomial L_{n}^{(α)}(x) has n real zeros with n1 positive zeros and 1 negative zero. However, for α lying in this range 2 < α < 1, the sequence {L_{n}^{(α)}(x)}_{n=0}^{∞} is NOT orthogonal with respect to any positive measure and, for each natural number n, the zeros of L_{n1}^{(α)}(x) DO NOT interlace with the zeros of L_{n}^{(α)}(x) for any natural number n. However, for each natural number n, the zeros of xL_{n1}^{(α)}(x) interlace with the zeros of L_{n}^{(α)}(x). The aim of the talk is to give some background to these results and raise open problems and questions that arise naturally. 

3:30 PM SDRICH 213 
Lund University 
Chebyshev polynomials A classical problem that goes back to Chebyshev and his study of mechanisms is to find the best uniform approximation of a continuous function f: [a,b]→R by algebraic polynomials of degree ≤n. It is well known that the monic degree n polynomial that deviates the least from zero on [1, 1] is given by
T_{n}(x)=2^{n+1}cos(nθ) with x=cos(θ). This polynomial oscillates for x between 1 and 1 and grows faster than any other monic polynomial of the same degree outside [1, 1]. But how can we describe the monic polynomials of least deviation from zero on E⊆R when E is the union of, say, k intervals or a Cantortype set? In the talk, I shall discuss the theory for these polynomials that also bear the name of Chebyshev. Since explicit representations are rare, I’ll focus on their asymptotic behavior and the asymptotics of the approximation error. One may ask how this depends on the size and geometry of E. As we shall see, potential theory enters the field and part of the analysis relies on studying the zeros in gaps of E. Towards the end, I shall also explain how relatively little is known when E is a closed region in the complex plane and discuss some open problems in the field. The talk is based on joint work with B. Simon (Caltech), P. Yuditskii (JKU Linz), and M. Zinchenko (UNM). 

3:30 PM SDRICH 213 
University of Vienna 
TBA TBA


3:30 PM SDRICH 213 
University of South Florida 
Stahl’s theorem on a Riemann surface H.Stahl’s theorem on convergence of Pade approximats for analytic functions with branch points [St861] [St861] is one of the fundamental results in the theory of rational approximations of analytic functions. It is also one of the basic facts in the theory of orthogonal pokynomilas. Denominators of Pade approximats are complex (nonhermittian) orthogonal polynomilas and Stahl’s created an original method of investigating asymptotics of complex orthogonal polynomials based directly on complex orthogonality.
The method has been further developed by A. Gonchar and E. Rakhmanov in [GR87] for the case of orthogonality with varying weight which is equivalnt to introduction of external field in associated equilibrium problem. Incorporation of the external field in the method makes circle of its application essentially larger. The GRSmethod may be applied to general rational interpolation, Hermite – Pade approximants (systems of interpolation conditions) and other constructions of freepole approximation by rational functions. Also the geometry of the problem in the presence of the external field becomes much more sophisticated. We generalize the method for the case of interpolation by meromorphic functions on a closed Riemann surface R which are, hence, algebraic functions. It turns out that basic results on zero distribution of poles of interpolating functions remain valid in essentially the same form. 

3:30 PM SDRICH 213 
NAM 
TBA TBA

DATE: April 24
SPEAKER: Mihai Stoiciu (Williams College)
TITLE: Random Unitary Matrices and Matrix Models for the Circular Beta Ensemble
ABSTRACT:
DATE: February 27
SPEAKER: Jiuyi Zhu (Louisiana State)
TITLE: Nodal sets of Robin and Neumann eigenfunctions
ABSTRACT:
DATE: November 28
SPEAKER: Jorge Arvesu (University Carlos III)
TITLE: On a construction of some rational approximants to ζ(n), n=2,3,…
ABSTRACT:
DATE: November 14
SPEAKER: Brian Simanek (Baylor University)
TITLE: Numerical Ranges, Blaschke Products, and Zeros of Orthogonal Polynomials
ABSTRACT:
DATE: November 7
SPEAKER: Cristina Pereyra (University of New Mexico)
TITLE: A tourist in the land of Hardy spaces (Equivalent definitions of Hardy spaces on product spaces of homogeneous type)
ABSTRACT:
DATE: October 17
SPEAKER: Guilherme Silva (University of Michigan)
TITLE: Products of Coupled Random Matrices
ABSTRACT:
In this talk we plan to briefly explain some motivations on why we should care about these products, discuss some recent developments when the matrices in the product are independent, and share some of the most recent findings, amongst others by the speaker together with Lun Zhang (Fudan University), in a model when the matrices being multiplied are not independent, but instead coupled in a useful way.
We will focus on asymptotic results obtained when the size of the matrices involved gets large, discussing both universal and nonuniversal features of the model, and in particular the emergence of the recently found MeijerG kernel. Some key elements in our analysis are a family of mixed type multiple orthogonal polynomials with respect to Bessel weights, and their zero asymptotic distribution which is described in terms of a constrained vector equilibrium problem.
DATE: September 26
SPEAKER: Chian Chuah (Baylor University)
TITLE: Fourier Multipliers on Free Groups along a Geodesic Path
ABSTRACT:
DATE: September 24 (Monday, 3:30PM SDRICH 207)
SPEAKER: Andrew Comech (Texas A&M and IITP, Moscow)
TITLE: Virtual levels, zeroenergy resonances, properties of virtual states, and the limiting absorption principle near thresholds
ABSTRACT:
(1) there are corresponding virtual states from the space slightly larger than L2;
(2) absence of the limiting absorption principle in the vicinity of the threshold point;
(3) bifurcation of eigenvalues from thresholds under a small perturbation.
We prove the equivalence of these definitions and study properties of corresponding virtual states. Once there is no virtual level, we study the limiting absorption principle near the threshold points, proving that, in the vicinity of a threshold, the resolvent is uniformly bounded in particular weighted spaces. We apply the theory to the Schroedinger operators, although the approach works for general nonselfadjoint operators (and in arbitrary dimension).
This is a joint work with Nabile Boussaid (Besançon) and Fritz Gesztesy (Baylor).
DATE: September 14 (Friday, 2:30PM SDRICH 207)
SPEAKER: Ian Wood (University of Kent)
TITLE: Embedding eigenvalues for periodic Jacobi operators using Wignervon Neumanntype perturbations
ABSTRACT:
DATE: September 12 (starting at 4:30)
SPEAKER: Malcolm Brown (Cardiff University)
TITLE: Spectral problems on star graphs
ABSTRACT:
The first step is a reduction to the problem on a single edge, but with an energy depending boundary condition at the vertex. In the second step, by means of an abstract inverse result for mfunctions, a reduction to a problem on a path graph with two edges, joined by continuity and Kirchhoff conditions, is given. All results are proved for symmetric linear relations in an orthogonal sum of Hilbert spaces. This ensures wide applicability to various different realisations, in particular, to canonical systems and Krein strings which include, as special cases, Dirac systems and Stieltjes strings. Employing two other key inverse results by de Branges and M. Krein, we answer the following question: If all differential operators are of one type, when can the reduced system be chosen to consist of two differential operators of the same type?
This is joint work with Heinz Langer and Christiane Tretter.
DATE: September 12
SPEAKER: Alan Czuron (University of Houston)
TITLE: On the isomorphisms of Fourier algebras of finite abelian groups
ABSTRACT:
We prove that if G_{1} and G_{2} are two infinite Vielenkin groups of bounded exponents such that G_{1} is not a subgroup of G_{2} then there are finite dimensional invariant convolution subalgebras of L^{1}(G_{1}) distant from any invariant convolution subalgebras of L^{1}(G_{2}). We show that the norm of certain class of algebraic isomorphims between them grows to infinity with the dimension.
DATE: September 5
SPEAKER: Andrew Fabian Celsus (Cambridge Center for Analysis)
TITLE: The Kissing Polynomials
ABSTRACT:
DATE: May 23
SPEAKER: Marcus Waurick (University of Strathclyde)
TITLE: On a theory for nonlocal homogenisation problems
ABSTRACT:
DATE: April 25
SPEAKER: Yulia Meshkova (St. Petersburg State)
TITLE: Operator error estimates for homogenization of elliptic and parabolic systems
ABSTRACT:
DATE: April 18
SPEAKER: No Seminar due to Barry Simon’s special lecture.
DATE: April 11
SPEAKER: Larry Harris (University of Kentucky)
TITLE: Alternation points, orthogonal polynomials and cubature
ABSTRACT:
p_{mn}(h_{j})=(1)^{j}p_{n}(h_{j})
for all j,n=0,…,m. For example, the Chebyshev points h_{j}=cos(jπ/m), for j=0,…,m are alternation points for the Chebyshev polynomials T_{0}, T_{1},…,T_{m}.
In this talk, we show that every finite decreasing sequence is a set of alternation points for some finite sequence of orthogonal polynomials and apply this to construct Lagrange polynomials and cubature formulas for the even and odd nodes of the Cartesian product of the points.
DATE: April 4
SPEAKER: Anna Vershynina (University of Houston)
TITLE: Introduction to Quantum Information
ABSTRACT:
DATE: March 21
SPEAKER: Li Gao (University of Illinois)
TITLE: Uncertainty Relation via Noncommutative L^{p}Space
ABSTRACT:
DATE: March 14
SPEAKER: Roger Nichols (University of Tennessee Chattanooga)
TITLE: The Limiting Absorption Principle for the Massless Dirac Operator
ABSTRACT:
DATE: March 7
SPRING BREAK: No Seminar
DATE: February 28
SPEAKER: Boris Hanin (Texas A&M)
TITLE: Random Waves and Remainder Estimates in the Weyl Law on a Compact Manifold
ABSTRACT:
DATE: February 21
SPEAKER: Alexander Pruss (Baylor University)
TITLE: Constructing probabilistically compatible conditionals
ABSTRACT:
If the algebra of sets has a probability measure, a plausible further axiom on conditionals is the Adams Thesis connecting conditionals and conditional probabilities: P(c(A,B)) = P(BA). There are a number of simple theorems showing that in the presence of various auxiliary assumptions, the Adams Thesis can only hold in trivial cases.
I show, however, that there is a natural collection of logical axioms on conditionals such that any probability space can be extended to a probability space on which there is a conditional satisfying the axioms and the Adams Thesis. The proof uses deep results in measure theory from the middle of the last century: the Maharam classification theorem and the von NeumannMaharam lifting theorem.
DATE: February 14
SPEAKER: Tao Mei (Baylor University)
TITLE: What are noncommutative L^{p} spaces?
ABSTRACT: This talk is a brief introduction on the socalled noncommutative L^{p} spaces. Two main examples will be those associated with matrices and discrete groups.
DATE: January 24
SPEAKER: Constanze Liaw (University of Delaware)
TITLE: Rank d Perturbations
ABSTRACT:
DATE: November 29
SPEAKER: HyunKyoung Kwon (University of Alabama)
TITLE: A similarity criteria for CowenDouglas operators
ABSTRACT:
DATE: November 22
THANKSGIVING BREAK: No Seminar
DATE: November 15
SPEAKER: Xiang Tang (Washington University in St. Louis)
TITLE: A new index theorem for monomial ideals by resolutions
ABSTRACT:
DATE: November 8
SPEAKER: Mark Ashbaugh (University of Missouri, Columbia)
TITLE: A Sharp Lower Bound for the First Eigenvalue of the Vibrating Clamped Plate under Compression
ABSTRACT:
This is joint work with Rafael Benguria (P. Universidad Catolica de Chile, Santiago) and Rajesh Mahadevan (Universidad de Concepcion, Chile).
DATE: October 18
SPEAKER: Isaac Michael (Baylor University)
TITLE: Birman’s Sequence of Inequalities and Their Relation to Generalized Continuous Cesaro Operators
ABSTRACT:
In this talk, we give a proof of this sequence of inequalities valid on a certain Hilbert space H_{n}([0,∞)) of functions defined on [0,∞). Moreover, f∈H_{n}([0,∞)) implies f^{‘}∈H_{n1}([0,∞)); as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman’s sequence. We also show that for any finite b>0, these inequalities hold on the standard Sobolev space H^{n}((0,b)). Furthermore, the Birman constants ((2n1)!!)^{2}/2^{2n} in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in L^{2}((0,∞)). We also show that these Birman constants are related to the norm of a generalized continuous Cesaro averaging operator.
DATE: October 12
SPEAKER: Helge Holden (Norwegian University of Science and Technology)
TITLE: What are the compact sets in Lebesgue spaces
ABSTRACT: We show an improvement of the classical KolomogorovRiesz theorem. This is joint work with Harald HancheOlsen and Eugenia Malinnikova (both at NTNU).
DATE: October 11
Notice: No seminar due to Frank Morgan’s colloquium
DATE: September 27
SPEAKER: Alexander Solynin (Texas Tech University)
TITLE: Image recognition, lemniscates, and quadratic differentials
ABSTRACT:
An interesting approach to fingerprint problem was suggested by Peter Ebenfelt, Dima Khavinson and Harold Shapiro in their paper Twodimensional shapes and lemniscates published in 2011. In this paper, the authors have shown, in particular, that fingerprints of polynomial lemniscates (which, by a classical result due to David Hilbert, are dense in the space of all twodimensional shapes) are generated by solutions of functional equations, which involve Blaschke products. A simpler proof of the main result of Ebenfelt, Khavinson and Shapiro and its generalization to the case of rational lemniscates was presented in a nice short paper Shapes, fingerprints and rational lemniscates by Malik Younsi published in 2016.
The first goal of this talk is to discuss how methods of Complex Analysis can be applied to the problems of pattern recognition. In particular, I will discuss the main results on fingerprints obtained by Ebenfelt, Khavinson and Shapiro and by Younsi. In addition, I will also mention a different approach to fingerprints via circle packing which was used by Brock Williams.
My second goal here is to present my recent results, which include as special cases the EbenfeltKhavinsonShapiro characterization of fingerprints of polynomial lemniscates as well as Younsi’s characterization of rational lemniscates. My main intention here is to emphasize the role of quadratic differentials in this developing theory.
DATE: September 20
SPEAKER: Matthew Fleeman (Baylor University)
TITLE: Hyponormal Toeplitz operators acting on the Bergman space
ABSTRACT:
DATE: September 13
SPEAKER: Tao Mei (Baylor University)
TITLE: Fourier multipliers on L^{p} spaces — the Mikhlin conditions
ABSTRACT:
DATE: September 6
SPEAKER: Paul Hagelstein (Baylor University)
TITLE: A Short Course on A^{p}weights III
ABSTRACT: Lecture 3 in a threepart series.
DATE: August 30
SPEAKER: Paul Hagelstein (Baylor University)
TITLE: A Short Course on A^{p}weights II
ABSTRACT: Lecture 2 in a threepart series.
DATE: August 23
SPEAKER: Paul Hagelstein (Baylor University)
TITLE: A Short Course on A^{p}weights I
ABSTRACT: Lecture 1 in a threepart series. The goal of the lecture series is to show that the HardyLittlewood maximal operator is bounded on L^{p}(w) if and only if w lies in the Muckenhoupt A_{p} class, via the reverseHolder inequality.
DATE: May 16 (2:303:30) (Note special date and time)
SPEAKER: Alexey Solyanik (Odessa Polytechnical University)
TITLE: Stabilization of Dynamical Systems and the Ranges of Complex Polynomials on the Unit Disk
ABSTRACT:
DATE: April 26
SPEAKER: Mehrdad Kalantar (University of Houston)
TITLE: Stationary C^{*}dynamical systems
ABSTRACT:
DATE: April 19
SPEAKER: Eric Ricard (University of Caen)
TITLE: Hilbert transforms – old and new stories
ABSTRACT:
DATE: April 18 from 3:304:30 (note special date and time)
SPEAKER: Ethan Gwaltney (Baylor University)
TITLE: A Probabilistic Proof of the Vitali Covering Lemma
ABSTRACT:
DATE: April 12 (4:00PM5:00PM)
SPEAKER: Selim Sukhtaiev (Univ. of Missouri)
TITLE: The Maslov index and the spectra of second order elliptic operators
ABSTRACT:
DATE: April 12
SPEAKER: Milivoje Lukic (Rice University)
TITLE: Higherorder Szego theorems and related problems
ABSTRACT:
DATE: March 29
SPEAKER: Michael Pang (University of Missouri)
TITLE: On (Conditional) Positive Semidefiniteness in the Matrix Valued Context
ABSTRACT:
DATE: March 22
SPEAKER: Dale Frymark (Baylor University)
TITLE: Boundary Conditions associated with the LeftDefinite Theory for Differential Operators
ABSTRACT:
DATE: March 15
SPEAKER: Roger Nichols (University of Tennessee Chattanooga)
TITLE: Krein’s Resolvent Identity and Boundary Data Maps for Regular Sturm–Liouville Operators
ABSTRACT:
DATE: March 8
SPRING BREAK: No Seminar
DATE: March 1
SPEAKER: Michael Brannan (Texas A&M)
TITLE: Radial multipliers and approximation properties for qArakiWoods algebras
ABSTRACT:
DATE: February 15
SPEAKER: Anton Zettl (Northern Illinois)
TITLE: Eigenvalues of SturmLiouville Problems with Periodic Coefficients
ABSTRACT:
DATE: February 1 (3:304:30)
SPEAKER: Tao Mei (Baylor University)
TITLE: Completely monotone functions, Markov semigroup generators, and functional calculus
ABSTRACT:
DATE: December 7
SPEAKER: Ioannis Parissis (University of the Basque Country)
TITLE: Asymptotic Estimates for Halo Sets and Applications
ABSTRACT: Click Here
DATE: November 30
SPEAKER: Erwin MinaDiaz (University of Mississippi)
TITLE: Asymptotics for polynomials orthogonal over a planar domain with holes
ABSTRACT:
∫_{D} P_{n}(z)P_{m}(z)dA(z)=δ_{n,m. }
The asymptotic behavior of P_{n}(z) as n→∞ has been investigated to a considerable extent, particularly when the region D is a simply connected domain bounded by a Jordan curve. In this work we investigate the situation when the domain of orthogonality is no longer simply connected but a multiply connected domain, trying to understand how the holes in the domain influence the asymptotic behavior of P_{n} inside D. Of particular interest is the canonical case of a circular multiply connected domain (CMCD) consisting of a disk with a finite number of mutually disjoint subdisks removed. We will also consider domains D that are conformally equivalent in a strong sense to a CMCD. This is a joint work with James Henegan.
DATE: November 16
SPEAKER: SangGyun Youn (Korean National University, visiting Texas A&M)
TITLE: HardyLittlewood inequality in compact quantum groups
ABSTRACT:
DATE: November 8
SPEAKER: Rob Milson (Dalhousie University)
TITLE: PseudoWronskians of Hermite polynomials
ABSTRACT:
DATE: October 25 (note special date)
SPEAKER: Richard Wellman (Westminster College)
TITLE: Differential Operators in Discrete Sobolev Spaces
ABSTRACT:
dμ = w + Σ_{j=0}^{n}(α_{j}δ_{a}^{(j)}+β_{j}δ_{b}^{(j)}) α_{j},β_{j}≥ 0; n ∈ N_{0}.
In particular Problem 10 asked for a ‘recipe’ for finding selfadjoint differential operators generated by a BochnerKrall spectral differential expression having the associated orthogonal polynomial sequence as eigenfunctions.
In this lecture we will discuss the history and motivation of this question and present a new GKNEM type theory that resolves this longstanding problem.
DATE: October 12
SPEAKER: Koushik Ramachandran (Oklahoma State University)
TITLE: Equidistribution of Zeros of Random Orthogonal Polynomials
ABSTRACT:
DATE: October 5
SPEAKER: Jameson Graber (Baylor University)
TITLE: Monotone operators and nonlinear semigroups
ABSTRACT:
DATE: September 28
SPEAKER: Matthew Fleeman (Baylor University)
TITLE: A brief survey of Hardy and Bergman Spaces
ABSTRACT:
DATE: September 21
SPEAKER: Tim Ferguson (University of Alabama)
TITLE: Extremal Problems for Analytic Functions and Their Connections to Other Topics
ABSTRACT:
DATE: September 7
SPEAKER: Jose Carrion (TCU)
TITLE: Topological invariants of groups obtained by deformations
ABSTRACT:
We will discuss previous and ongoing work with Marius Dadarlat that elucidates this connection further. In fact, regarded in the right light, the answer comes from an index theory calculation that relates deformations of the fundamental group Z^{2} of the twotorus with “almost flat” bundles over the twotorus. In this context, the theory generalizes to other surface groups, and beyond.
DATE: August 2 at 3:30
SPEAKER: Kelly Bickel (Bucknell University)
TITLE: Compressions of the shift on twovariable model spaces
ABSTRACT:
DATE: May 31
SPEAKER: Quanhua Xu (University de Franche Comte)
TITLE: Maximal Inequalities in Noncommutative Analysis
ABSTRACT: Click Here
DATE: April 26 at 4:00PM
SPEAKER: Jorge Arvesu (Universidad Carlos III de Madrid)
TITLE: Vector equilibrium problem with constraint and n^{th} root asymptotics for some multiple orthogonal polynomials
ABSTRACT:
DATE: April 20
SPEAKER: Zhizhang Xie (Texas A&M University)
TITLE: Applications of finite dynamic asymptotic dimension to algebraic Ktheory
ABSTRACT:
DATE: April 13
SPEAKER: Paul Hagelstein (Baylor University)
TITLE: Solyanik Estimates in Harmonic Analysis
ABSTRACT:
M_{B}f(x) = sup_{x ∈ R ∈ B}∫_{R}f.
For 0 <α< 1, the associated Tauberian constant C_{B}(α) is given by
C_{B}(α) = sup_{E ⊆ ℝn : 0 <E< ∞}{x ∈ ℝ^{n} : M_{B}χ_{E}(x)>α}/E.
A maximal operator M_{B} such that lim_{α → 1–}C_{B}(α) = 1 is said to satisfy a Solyanik estimate.
In this talk we will prove that the uncentered HardyLittlewood maximal operator satisfies a Solyanik estimate. Moreover, we will indicate applications of Solyanik estimates to smoothness properties of Tauberian constants and to weighted norm inequalities. We will also discuss several fascinating open problems regarding Solyanik estimates. This research is joint with Ioannis Parissis.
DATE: April 11 at 3:30PM in SDRICH 207
SPEAKER: Malcolm Brown (Cardiff University)
TITLE: Uniqueness for an inverse problem in electromagnetism with partial data
ABSTRACT:
DATE: April 6
SPEAKER: Braxton Osting (University of Utah)
TITLE: Dirichlet graph partitions
ABSTRACT:
DATE: March 9
SPRING BREAK: No Seminar
DATE: March 2
SPEAKER: Constanze Liaw (Baylor University)
TITLE: Cyclic vectors in Dirichlet type spaces and optimal approximants
ABSTRACT:
A function f(z) is said to be cyclic in D_{α} if the sequence of forward orbits z^{k} f(z), k∈{0,1,2,…}, has a dense span in D_{α}. Since the constant function g=1 is cyclic, we set out on an endeavor to learn about the approximation of the function 1 by functions of the form p_{n} f for fixed f∈ D_{α} and polynomials p_{n} of varying degrees n.
DATE: February 16 at 3:30
SPEAKER: Eric Ricard (University of Caen)
TITLE: Hypercontractivity for Free Groups
ABSTRACT:
DATE: January 20
SPEAKER: Maxim Derevyagin (University of Mississippi)
TITLE: Spectral transformations in the theory of orthogonal polynomials
ABSTRACT:
In my talk I’m going to discuss some nonclassical situations in regard to spectral transformations of orthogonal polynomials on the real line. Namely, I’ll start with showing how spectral transformations help to deal with signed measures with one sign change and with the corresponding nonsymmetric tridiagonal matrices. In particular, the theory of such matrices brings us to the context of Padé approximation and, more importantly, the behavior of spurious poles of Padé approximants at infinity for Cauchy transforms of signed measures with one sign change is fully characterized. Then, we’ll see that to get such results for signed measures with several sign changes and other singularities one needs to consider multiple Christoffel and Geronimus transformations. Finally, it’ll be demonstrated that multiple Geronimus transformations could lead to Sobolev orthogonal polynomials.
DATE: December 2
SPEAKER: Dale Frymark (Baylor University)
TITLE: Iterated RankOne Perturbations and Absence of Extended States
ABSTRACT:
DATE: November 18
SPEAKER: Tom Alberts (University of Utah)
TITLE: Random Geometry in the Spectral Measure of the Circular Beta Ensemble
ABSTRACT:
DATE: November 11
SPEAKER: Rongwei Yang (University of Albany and Texas A&M)
TITLE: Joint spectrum for noncommuting operators
ABSTRACT:
DATE: November 4
SPEAKER: Paul Hagelstein (Baylor University)
TITLE: (postponed; new date is TBD)
ABSTRACT:
DATE: October 28
SPEAKER: Bill Beckner (University of Texas at Austin)
TITLE: Inequalities in Fourier Analysis and Measures for Fractional Smoothing
ABSTRACT:
DATE: October 21
SPEAKER: David Blecher (University of Houston)
TITLE: Generalizing positivity techniques in Banach and operator algebras
ABSTRACT:
DATE: October 14
SPEAKER: Tao Mei (Baylor University)
TITLE: Riesz transforms associated with cocycles and Hormander Fourier multipliers on OUMD spaces
ABSTRACT:
DATE: October 7
SPEAKER: Lance Littlejohn (Baylor University)
TITLE: GlazmanKreinNaimark Theory, LeftDefinite Theory and the Square of the Legendre Polynomials Differential Operator
ABSTRACT:
operator A in L^{2}(1,1) having the Legendre polynomials {P_{n}}_{n=0}^{∞} as eigenfunctions. As a particular consequence, they explicitly determine the domain D(A^{2}) of the selfadjoint operator A^{2}. However, this domain, in their characterization, does not contain boundary conditions. In fact, this is a general feature of the leftdefinite approach developed by Littlejohn and Wellman. Yet, the square of the secondorder Legendre expression is in the limit4 case at each end point x = ± 1 in L^{2}(1,1) meaning that D(A^{2}) should exhibit four boundary conditions. In this talk, after a gentle ‘crash course’ on leftdefinite theory and the classical GlazmanKreinNaimark (GKN) theory, we show that D(A^{2}) can, in fact, be expressed using four (separated) boundary conditions. In addition, we determine a new characterization of D(A^{2}) that involves four nonGKN boundary conditions. These new boundary conditions are surprisingly simple – and natural – and are equivalent to the boundary conditions obtained from the GKN theory.
DATE: September 30
SPEAKER: Yunyun Yang (Baylor University)
TITLE: Thick distributions, asymptotic expansion of distributions, and spectral asymptotics
ABSTRACT:
DATE: September 23
SPEAKER: Brian Simanek (Baylor University)
TITLE: Extremal Polarization Configurations for Integrable Kernels
ABSTRACT:
DATE: September 16
SPEAKER: Brian Simanek (Baylor University)
TITLE: An Introduction to Minimum Energy Problems
ABSTRACT: