Displaying similar documents to “On Fourier coefficients and factorable operators.”

A characterization of Fourier transforms

Philippe Jaming (2010)

Colloquium Mathematicae

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The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.

On the Fourier transform, Boehmians, and distributions

Dragu Atanasiu, Piotr Mikusiński (2007)

Colloquium Mathematicae

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We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.

Algebrability of the set of non-convergent Fourier series

Richard M. Aron, David Pérez-García, Juan B. Seoane-Sepúlveda (2006)

Studia Mathematica

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We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.

Inverse Fourier transform

Leonede De Michele, Marina Di Natale, Delfina Roux (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper a very general method is given in order to reconstruct a periodic function f knowing only an approximation of its Fourier coefficients.