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Diffraction theory and almost periodic distributions

journal contribution
posted on 2023-05-19, 04:50 authored by Strungaru, N, Venta TeraudsVenta Terauds
We introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distribution. We further introduce the spaces of weakly, strongly and null weakly almost periodic tempered distributions and show that for weakly almost periodic tempered distributions the Eberlein decomposition holds. For translation bounded measures all these notions coincide with the classical ones.We show that tempered distributions with measure Fourier transform are weakly almost periodic and that for this class, the Eberlein decomposition is exactly the Fourier dual of the Lebesgue decomposition, with the Fourier–Bohr coefficients specifying the pure point part of the Fourier transform. We complete the project by looking at few interesting examples.

History

Publication title

Journal of Statistical Physics

Volume

164

Issue

5

Pagination

1183-1216

ISSN

0022-4715

Department/School

School of Natural Sciences

Publisher

Kluwer Academic/Plenum Publ

Place of publication

233 Spring St, New York, USA, Ny, 10013

Rights statement

Copyright 2016 Springer Science+Business Media New York

Repository Status

  • Restricted

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