The growth of laguerre matrix polynomials on bounded intervals |
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Authors: | L. J dar,J. Sastre |
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Affiliation: | Departamento de Matemática Aplicada Universidad Politécnica de Valencia, Valencia, Spain Departamento de Comunicaciones Universidad Politécnica de Valencia, Valencia, Spain |
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Abstract: | Let A be a matrix in r×r such that Re(z) > −1/2 for all the eigenvalues of A and let {πn(A,1/2) (x)} be the normalized sequence of Laguerre matrix polynomials associated with A. In this paper, it is proved that πn(A,1/2) (x) = O(n(A)/2lnr−1(n)) and πn+1(A,1/2) (x) − πn(A,1/2) (x) = O(n((A)−1)/2lnr−1(n)) uniformly on bounded intervals, where (A) = max{Re(z); z eigenvalue of A}. |
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Keywords: | Laguerre matrix polynomials Gamma function Asymptotics |
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