Compact Jacobi matrices : from Stieltjes to Krein and $M(a, b)$

Walter Van Assche

Displaying similar documents to “Compact Jacobi matrices : from Stieltjes to Krein and $M (a, b)$ ”

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.

Nonnegative linearization for orthogonal polynomials with eventually constant Jacobi parameters

Wojciech Młotkowski (2010)

Banach Center Publications

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We study the nonnegative product linearization property for polynomials with eventually constant Jacobi parameters. For some special cases a necessary and sufficient condition for this property is provided.

Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials

Marčoková, Mariana, Guldan, Vladimír

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In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them. We derive expressions of generalized Legendre polynomials and generalized ultraspherical polynomials by means of classical Jacobi polynomials.

Products of several Jacobi or Laguerre polynomials

Bruno Gabutti (1984)

Rendiconti del Seminario Matematico della Università di Padova

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On a Szegö's theorem of orthogonal polynomials.

Jesús Sánchez Dehesa (1979)

Revista Matemática Hispanoamericana

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It is found that the asymptotical density of zeros of a system of orthogonal polynomials whose weight function belongs to a wide class of distribution functions has the expression ρ(x) = π (1 - x). This result is shown in two completely different ways: (1) from a Szegö theorem and (2) from a Geronimus theorem and a finding recently obtained by the author in a context of Jacobi matrices.