Displaying similar documents to “Bernoulli convolutions-an application of set theory in analysis”

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.

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.

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales UMCS, Mathematica

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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.

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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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.