Results 1 to 10 of about 1,874,872 (323)
Ratio Asymptotics for Orthogonal Matrix Polynomials
Journal of Approximation Theory, 1999 In the 1979's monograph ``Orthogonal polynomials'' [Mem. Am. Math. Soc. 213, 185 p. (1979; Zbl 0405.33009)] \textit{P. Nevai} established a remarkable result that orthogonal polynomials on \(\mathbb R\), satisfying a 3-term recurrence relation with converging coefficients, present a ratio asymptotics outside of the set of accumulation points of the ...
Antonio J Duran
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Finite Orthogonal M Matrix Polynomials [PDF]
SymmetryIn this study, we aim to construct a finite set of orthogonal matrix polynomials for the first time, along with their finite orthogonality, matrix differential equation, Rodrigues’ formula, several recurrence relations including three-term relation, forward and backward shift operators, generating functions, integral representation and their relation ...
Esra Güldoğan Lekesız
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A matrix approach for the semiclassical and coherent orthogonal polynomials [PDF]
Applied Mathematics and Computation, 2015 We obtain a matrix characterization of semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthogonal polynomials, and the lower triangular matrix that represents the orthogonal polynomials in terms of the monomial basis of polynomials.
Luis E Garza +2 more
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An evolution of matrix-valued orthogonal polynomials [PDF]
Pacific Journal of Mathematics21 pages, 3 ...
Erik Koelink +2 more
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Orthogonal matrix polynomials and applications
Journal of Computational and Applied Mathematics, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Walter van Assche
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Orthogonal matrix polynomials whose differences are also orthogonal
Journal of Approximation Theory, 2014 We characterize orthogonal matrix polynomials (Pn)n whose differences (∇Pn+1)n are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn)n are orthogonal. We also construct some illustrative examples.
Antonio José Durán Guardeño
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Szegő’s theorem for matrix orthogonal polynomials
Journal of Approximation Theory, 2012 We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szegő's theorem. As a by-product, we also obtain an elementary proof of the distance formula by Helson and Lowdenslager.
Sergey Khrushchev +2 more
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Matrix Orthogonal Polynomials: A Riemann--Hilbert approach [PDF]
, 2023 In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain information about the matrix orthogonal polynomials and functions of second kind associated with a weight matrix. We deduce properties for the recurrence relation coefficients from differential properties of the weight matrix.
Amílcar Branquinho +3 more
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Uvarov perturbations for matrix orthogonal polynomials
Proceedings of the American Mathematical Society, Series BAdditive perturbations, specifically matrix Uvarov transformations for matrix orthogonal polynomials, are under consideration. Christoffel–Uvarov formulas are deduced for the perturbed biorthogonal families, along with their matrix norms. These formulations are expressed in terms of the spectral jets of the Christoffel–Darboux kernels.
Gerardo Ariznabarreta +3 more
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On Laguerre-Sobolev matrix orthogonal polynomials
Open MathematicsIn this manuscript, we study some algebraic and differential properties of matrix orthogonal polynomials with respect to the Laguerre-Sobolev right sesquilinear form defined by ⟨p,q⟩S≔∫0∞p*(x)WLA(x)q(x)dx+M∫0∞(p′(x))*W(x)q′(x)dx,{\langle p,q\rangle }_ ...
Fuentes Edinson +2 more
doaj +2 more sources