From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory

Preface.- Compositions and Chebyshev Polynomials.- Non-negative Extensions of Hamiltonian Systems.- On Simon’s Hausdorff Dimension Conjecture.- Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures.- Ballistic Transport for Periodic Jacobi Operators on Zd.- Perspectives on General Left-Definite Theory.- Sampling in the range of the analysis operator of a continuous frame having unitary structure.- An extension of the coherent pair of measures of the second kind on the unit circle.- Bessel-Type Operators and a Refinement of Hardy’s Inequality.- Spectral Theory of Exceptional Hermite Polynomials.- Occupation time for classical and quantum walks.- On foci of ellipses inscribed in cyclic polygons.- A Differential Analogue of Favard’s Theorem.- Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces.- The BFK-gluing formula for zeta-determinants and the conformal rescaling of a metric.- New representations of the Laguerre–Sobolev and Jacobi–Sobolev orthogonal polynomials.- Compactness, or Lack Thereof, for the Harmonic Double Layer.- Weighted Chebyshev Polynomials on Compact Subsets of the Complex Plane.- The Eichler integral of E2 and q-brackets of t-hook functions.