On Fourier re-expansions

Details On Fourier re-expansions On Fourier re-expansions

2012-01-20

arxiv.org/abs/1201.4217v1

Mathematics

Classical Analysis and ODEs

9 pages

Scientific paper

We study an extension to Fourier transforms of the old problem on absolute
convergence of the re-expansion in the sine (cosine) Fourier series of an
absolutely convergent cosine (sine) Fourier series. The results are obtained by
revealing certain relations between the Fourier transforms and their Hilbert
transforms.

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