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Equiconvergence and equisummability of Jacobi series

Boychev, Georgi (2011)

Serdica Mathematical Journal

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

Equiconvergence theorems for Laguerre series

Georgi Karadzhov (1992)

Banach Center Publications

The Szegö equiconvergence theorem for the Laguerre series is improved. In particular, a system of exact sufficient conditions is given.

Esterlè's proof of the tauberian theorem for Beurling algebras

H. G. Dales, W. K. Hayman (1981)

Annales de l'institut Fourier

Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for L 1 ( R ) using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane. We here use essentially the same method to prove the analogous result for Beurling algebras L φ 1 ( R ) . Our estimates need a theorem of Hayman and Korenblum.

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