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A generalization of formulas for the discriminants of quasi-orthogonal polynomials with applications to hypergeometric polynomials
In this article, we extend the classical framework for computing discriminants of special quasi-orthogonal polynomials from Schur’s resultant...
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Matrix orthogonal polynomials, non-abelian Toda lattices, and Bäcklund transformations
A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper. The normalization factors of...
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Three term relations for multivariate Uvarov orthogonal polynomials
Three term relations for orthogonal polynomials in several variables associated to a moment linear functional obtained by a Uvarov modification of a...
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Pearson equations for discrete orthogonal polynomials: III—Christoffel and Geronimus transformations
Contiguous hypergeometric relations for semiclassical discrete orthogonal polynomials are described as Christoffel and Geronimus transformations....
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Electrostatic Partners and Zeros of Orthogonal and Multiple Orthogonal Polynomials
For a given polynomial P with simple zeros, and a given semiclassical weight w , we present a construction that yields a linear second-order...
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QBD Processes Associated with Jacobi–Koornwinder Bivariate Polynomials and Urn Models
We study a family of quasi-birth-and-death (QBD) processes associated with the so-called first family of Jacobi–Koornwinder bivariate polynomials....
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Ehrhart Quasi-Polynomials of Almost Integral Polytopes
A lattice polytope translated by a rational vector is called an almost integral polytope. In this paper, we study Ehrhart quasi-polynomials of almost...
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Spectral transformations and second kind polynomials associated with a hermitian linear functional
The aim of this paper is to analyze the relation between the Christoffel transformations in the framework of hermitian linear functionals and the...
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Spectral properties related to generalized complementary Romanovski–Routh polynomials
Complementary Romanovski–Routh polynomials play an important role in extracting specific properties of orthogonal polynomials. In this work, a...
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Classical Orthogonal Polynomials Revisited
This manuscript contains a small portion of the algebraic theory of orthogonal polynomials developed by Maroni and their applicability to the study...
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Quasi-orthogonal cocycles, optimal sequences and a conjecture of Littlewood
A quasi-orthogonal cocycle, defined over a group of order congruent to 2 modulo 4, is naturally analogous to an orthogonal cocycle (i.e., one defined...
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Numerical Methods and Applications 10th International Conference, NMA 2022, Borovets, Bulgaria, August 22–26, 2022, Proceedings
This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications,...
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Intersection theoretic inequalities via Lorentzian polynomials
We explore the applications of Lorentzian polynomials to the fields of algebraic geometry, analytic geometry and convex geometry. In particular, we...
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Multiplication operator and average characteristic polynomial associated with exceptional Jacobi polynomials
Studying the multiplication operator associated with exceptional Jacobi polynomials, the zero distribution of the corresponding average...
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Positivity and Positivity-Definiteness for Cauchy Powers of Linear Functionals on the Linear Space of Polynomials
In this paper, an exploration is undertaken into positivity and positivity-definiteness within the Cauchy product and self-product, which encompass...
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Bivariate Koornwinder–Sobolev Orthogonal Polynomials
The so-called Koornwinder bivariate orthogonal polynomials are generated by means of a non-trivial procedure involving two families of univariate...
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Exceptional collections for mirrors of invertible polynomials
We prove the existence of a full exceptional collection for the derived category of equivariant matrix factorizations of an invertible polynomial...