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

Jan Persson

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

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

Yngve Domar (1970)

Annales de l'institut Fourier

Similarity:

Let $μ$ be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on $R$ . Then for every $ϵ > 0$ , ${x \in R | Re (μ (x)) > ϵ}$ has a vanishing interior Lebesgue measure. If $ϵ = 0$ the statement is not generally true. The result is applied to prove a theorem of Rosenthal.

A Note on Multipliers for Integrable Boehmians

Nemzer, Dennis (2009)

Fractional Calculus and Applied Analysis

Similarity:

2000 Mathematics Subject Classification: 44A40, 42A38, 46F05 The product of an entire function satisfying a growth condition at infinity and an integrable Boehmian is defined. Properties of this product are investigated.

Series expansions for Fourier transforms and Lebesgue functions

Raimond Struble (1984)

Studia Mathematica

Similarity:

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales UMCS, Mathematica

Similarity:

Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.