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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 ...
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. ...
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. ...
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 ...
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 ...
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 , ...
Spherical Functions of Fundamental K-Types Associated with the n-Dimensional Sphere
(Natl Acad Sci Ukraine, 2014-01)
In this paper, we describe the irreducible spherical functions of fundamentalK-types associated with the pair (G, K) = (SO(n + 1), SO(n)) in terms of matrix hypergeometric functions. The output of this description is that ...
Bispectrality and Time-Band-Limiting: Matrix valued polynomials
(Oxford University Press, 2018-05)
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturallyappearing integral operator admits a commuting dierential one, allowing for a numerically ecient way to compute ...
Bispectrality and time-band limiting: Matrix-valued polynomials
(Oxford University Press, 2018-06)
The subject of time-band limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to ...
Time and band limiting for matrix valued functions: An integral and a commuting differential operator
(IOP Publishing, 2017-01-09)
The problem of recovering a signal of finite duration from a piece of its Fourier transform was solved at Bell Labs in the 1960's, by exploiting a 'miracle': a certain naturally appearing integral operator commutes with ...