On The Fourier Transform And The Exchange Property

A simplified construction of tempered Boehmians is presented. The new construction shows that considering delta sequences and convergence arguments is not essential. Copyright © 2005 Hindawi Publishing Corporation

On The Fourier Transform, Boehmians, And Distributions

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

The Fourier Transform Of Levy Measures On A Semigroup

Using completely positive-definite functions defined on a commutative semigroup, we construct a space of pseudoquotients that can be identified, via a Fourier transform, with a class of Lévy measures. As an application we obtain a generalization of the Lévy-Khinchin representation for completely alternating functions

Fourier Transform Of Radon Measures On A Locally Compact Group

A space of generalized functions is constructed that allows us to generalize Bochner\u27s theorem so that all Radon measures on a locally compact group are in a one-to-one correspondence with elements of that space of generalized functions. This defines a Fourier transform for all Radon measures on a locally compact group. © 2010 Taylor & Francis