A spectral Paley-Wiener theorem

Abstract

The Fourier inversion formula in polar form is {Mathematical expression} for suitable functions f on ℝn, where Pλf(x) is given by convolution of f with a multiple of the usual spherical function associated with the Euclidean motion group. In this form, Fourier inversion is essentially a statement of the spectral theorem for the Laplacian and the key question is: how are the properties of f and Pλf related? This paper provides a Paley-Wiener theorem within this avenue of thought generalizing a result due to Strichartz and provides a spectral reformulation of a Paley-Wiener theorem for the Fourier transform due to Helgason. As an application we prove support theorems for certain functions of the Laplacian. © 1993 Springer-Verlag.

Document Type

Article

DOI

https://doi.org/10.1007/BF01388416

Publication Date

3-1-1993

Journal Title

Monatshefte für Mathematik

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