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ArticleOriginal scientific text

Title

Polyhedral summability of multiple Fourier series (and explicit formulas for Dirichlet kernels on ^n and on compact Lie groups)

Authors 1

Affiliations

  1. Dipartimento di Matematica, Politecnico di Torino, Corso Duca Degli Abruzzi, 24 10129 Torino, Italy

Abstract

We study polyhedral Dirichlet kernels on the n-dimensional torus and we write a fairly simple formula which extends the one-dimensional identity ∑j=-NNeijt=sin((N+(12))t)sin((12)t). We prove sharp results for the Lebesgue constants and for the pointwise boundedness of polyhedral Dirichlet kernels; we apply our results and methods to approximation theory, to more general summability methods and to Fourier series on compact Lie groups, where we write an asymptotic formula for the Dirichlet kernels.

Keywords

ENG
polyhedral Dirichlet kernels, multiple Fourier series, Fourier series on compact Lie groups, Lebesgue constants

Bibliography

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Colloquium Mathematicum
1993/65/1
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Pages:
103-116
Main language of publication
English
Received
1992-05-26
Accepted
1992-11-26
Published
1993
Exact and natural sciences