A property of Fourier Stieltjes transforms on the discrete group of real numbers

Yngve Domar

Displaying similar documents to “A property of Fourier Stieltjes transforms on the discrete group of real numbers”

Operational calculus and Fourier transform on Boehmians

V. Karunakaran, R. Roopkumar (2005)

Colloquium Mathematicae

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We define various operations on the space of ultra Boehmians like multiplication with certain analytic functions which are Fourier transforms of compactly supported distributions, polynomials, and characters $(e^{i s t}, s, t \in ℝ)$ , translation, differentiation. We also prove that the Fourier transform on the space of ultra Boehmians has all the operational properties as in the classical theory.

The Fourier transform on $L_{loc}^{1}$ and its application to Cauchy problems for linear partial differential equations

Jan Persson (1971)

Rendiconti del Seminario Matematico della Università di Padova

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On functions whose translates are independent

Ralph E. Edwards (1951)

Annales de l'institut Fourier

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Ce travail est l’étude de divers cas particuliers d’un problème nouveau, semble-t-il, concernant les translatées de fonctions ou de distributions sur un groupe. Soit $E$ un espace vectoriel topologique de fonctions ou de distributions sur un groupe abélien $G$ localement compact ; $E$ est supposé invariant par les translations $a \to f_{a} (x) = f (x + a) (f \in E, a \in G)$ . Si $f \in E$ et si $A$ est un sous-ensemble non vide de $G$ , $I (f, A) = I (f, A, E)$ désigne le sous-espace vectoriel fermé de $E$ engendré par les translatées $f_{a}$ de $f$ avec $a \in A$ . On dira qu’une $f \in E$ a ses...

A stable method for the inversion of the Fourier transform in $R^{N}$

Leonede De Michele, Delfina Roux (1993)

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

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A general method is given for recovering a function $f : R^{N} \to C$ , $N \geq 1$ , knowing only an approximation of its Fourier transform.

On the subspace of $L^{p}$ invariant under multiplication of transform by bounded continuous functions

Alessandro Figà-Talamanca (1965)

Rendiconti del Seminario Matematico della Università di Padova

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Comparison theorem between Fourier transform and Fourier transform with compact support

Christine Huyghe (2013)

Journal de Théorie des Nombres de Bordeaux

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We prove a comparison theorem between Fourier transform without support and and Fourier transform with compact support in the context of arithmetic $𝒟$ -modules.

The support of a function with thin spectrum

Kathryn Hare (1994)

Colloquium Mathematicae

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We prove that if $E \subseteq Ĝ$ does not contain parallelepipeds of arbitrarily large dimension then for any open, non-empty $S \subseteq G$ there exists a constant c > 0 such that $∥ f 1_{S} ∥_{2} \geq c ∥ f ∥_{2}$ for all $f \in L^{2} (G)$ whose Fourier transform is supported on E. In particular, such functions cannot vanish on any open, non-empty subset of G. Examples of sets which do not contain parallelepipeds of arbitrarily large dimension include all Λ(p) sets.

A characterization of the minimal strongly character invariant Segal algebra

Viktor Losert (1980)

Annales de l'institut Fourier

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For a locally compact, abelian group $G$ , we study the space $S_{0} (G)$ of functions on $G$ belonging locally to the Fourier algebra and with $l^{1}$ -behavior at infinity. We give an abstract characterization of the family of spaces ${S_{0} (G) : G$ abelian $}$ by its hereditary properties.