Displaying similar documents to “On the orthogonality of sorne systems of polynornials.”

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D. Mangeron, A. M. Krall, D. L. Fernández (1983)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Operators preserving orthogonality of polynomials

Francisco Marcellán, Franciszek Szafraniec (1996)

Studia Mathematica

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Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions...

On block recursions, Askey's sieved Jacobi polynomials and two related systems

Bernarda Aldana, Jairo Charris, Oriol Mora-Valbuena (1998)

Colloquium Mathematicae

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Two systems of sieved Jacobi polynomials introduced by R. Askey are considered. Their orthogonality measures are determined via the theory of blocks of recurrence relations, circumventing any resort to properties of the Askey-Wilson polynomials. The connection with polynomial mappings is examined. Some naturally related systems are also dealt with and a simple procedure to compute their orthogonality measures is devised which seems to be applicable in many other instances.