Displaying similar documents to “A Cohen type inequality for Fourier expansions of orthogonal polynomials with a nondiscrete Jacobi-Sobolev inner product.”

Under which conditions is the Jacobi space L w ( a , b ) p [ - 1 , 1 ] subset of L w ( α , β ) 1 [ - 1 , 1 ] ?

Michael Felten (2007)

Open Mathematics

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Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property L w ( a , b ) p [ - 1 , 1 ] ⊂ L w ( α , β ) 1 [ - 1 , 1 ] is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.

Equiconvergence and equisummability of Jacobi series

Boychev, Georgi (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 33C45, 40G05. In this paper we give some results concerning the equiconvergence and equisummability of series in Jacobi polynomials.

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.