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Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
(Springer, 2017-06)
Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised ...
Chapter 7: A further look at time-and-band limiting for matrix orthogonal polynomials
(World Scientific Publishing Co, 2018)
We extend to a situation involving matrix-valued orthogonal polynomials, a scalar result that originates in work of Shannon and a ground-breaking series of papers by Slepian, Landau and Pollak at Bell Labs in the 1960s. ...
Ladder relations for a class of matrix valued orthogonal polynomials
(Wiley Blackwell Publishing, Inc, 2021-02)
Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on (Formula presented.), and we ...
Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice
(Academic Press Inc Elsevier Science, 2019-09)
A general family of matrix valued Hermite type orthogonal polynomials is introduced as the matrix orthogonal polynomials with respect to a weight. The matrix polynomials are eigenfunctions of a matrix differential equation. ...
Emergence of power law distributions for odd and even lifetimes
(American Physical Society, 2020-12-24)
Avalanche lifetime distributions have been related to first-return random walk processes. In this sense, the theory for random walks can be employed to understand, for instance, the origin of power law distributions in ...
On the use of orthogonal polynomials in the study of anisotropic plates
(Academic Press Ltd - Elsevier Science Ltd, 2003-07-24)
After Walter Ritz had presented in 1908 his now famous variational method, interest was particularly shown by several mathematicians from whom the substantiation of the method has received lengthy treatment [1–5]. On the ...
On the measure of polynomials attaining maxima on a vertex
(Element, 2019-03)
We calculate the probability that a k-homogeneous polynomial in n variables attain a local maximum on a vertex in terms of the “sharpness” of the vertex, and then study the dependence of this measure on the growth of ...
Matrix elements of irreducible representations of SU(n + 1)×SU(n + 1) and multivariable matrix-valued orthogonal polynomials
(Academic Press Inc Elsevier Science, 2020-04-15)
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking ...
2 × 2 hypergeometric operators with diagonal eigenvalues
(Academic Press Inc Elsevier Science, 2019-12)
In this work we give all the order-two hypergeometric operators D, symmetric with respect to some 2 × 2 irreducible matrix-weight W on (0,1) such that DPn=Pnλn00μn with no repetition among the eigenvalues {λn,μn}n∈N0 , ...