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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 , ...
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. ...
Induced Sputum MMP-1, -3 & -8 Concentrations during Treatment of Tuberculosis
(Public Library of Science, 2013)
Introduction: Tuberculosis (TB) destroys lung tissues and this immunopathology is mediated in part by Matrix Metalloproteinases (MMPs). There are no data on the relationship between local tissue MMPs concentrations, ...
Weak matrix majorization
(Elsevier Science Inc, 2005-07)
Given X, Y ∈ Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization, X≻ w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = Y, and consider the relations between this ...
Hyperbolicity of the Karcher mean
(Elsevier Science Inc., 2022-02)
The main concern of this paper is the Karcher mean of linearly independent triples (A,B,C) on the hyperbolic manifold of 2×2 positive definite matrices of determinant 1. We show that the Karcher mean is of the form ...
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 ...
The Karcher mean of linearly independent triples
(Elsevier Science Inc, 2021-02)
We present a classification of 2×2 positive definite Hermitian triples of determinant one having the Karcher mean formula [Formula presented]. We further show that it is equivalent to the trace condition: tr(AB−1)=tr(AC− ...
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 ...
Generalized apostol-type polynomial matrix and its algebraic properties
(Mathematical Reports, 2019)
Euler matrices and their algebraic properties revisited
(Applied Mathematics and Information Sciences, 2020)