Mathematics, Department of
Department of Mathematics: Faculty Publications
Accessibility Remediation
If you are unable to use this item in its current form due to accessibility barriers, you may request remediation through our remediation request form.
Document Type
Article
Date of this Version
1971
Citation
Bulletin Of The American Mathematical Society Volume 77, Number 3, May 1971
Abstract
The resulting "Fourier transformation" µ—µ^ contains the classical theory and leads to generalizations of a variety of classical results, including the Plancherel theorem and the Poisson summation formula. The present work can also be regarded as a sort of theory of tempered distributions on general locally compact abelian groups. It is true that Bruhat [ l l ] introduced a direct generalization to this setting of the theory of Schwartz [10], but, to the best of our knowledge, a detailed study of the Fourier transform has not been carried out. In a forthcoming exposition we shall describe the precise relation between the present study and the work of Bruhat.
Comments
Copyright ® 1971, American Mathematical Society