منابع مشابه
Matrix-valued little q-Jacobi polynomials
Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2 × 2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and its relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on the m...
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A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step recurrence relation, integral inter-relations, and quasi-orthogonality relations. 1. Motivation The understanding of matrix-valued orthogonal polynomi...
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Consider the Jacobi operators J given by (J y)n = anyn+1+bnyn+a∗n−1yn−1, yn ∈ C (here y0 = yp+1 = 0), where bn = b ∗ n and an : det an 6= 0 are the sequences of m × m matrices, n = 1, .., p. We study two cases: (i) an = a∗n > 0; (ii) an is a lower triangular matrix with real positive entries on the diagonal (the matrix J is (2m+1)-band mp×mp matrix with positive entries on the first and the las...
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Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrix r new rows and columns, so that the original Jacobi matrix is shifted downward. The r new...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2003
ISSN: 0007-4497
DOI: 10.1016/s0007-4497(03)00009-5