Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Finite Fourier self-transforms

Authors: A. Fedotowsky and G. Boivin
Journal: Quart. Appl. Math. 30 (1972), 235-254
MSC: Primary 42A60
DOI: https://doi.org/10.1090/qam/422988
MathSciNet review: 422988
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Abstract: This paper considers the integral equation

$\displaystyle \lambda \gamma \left( {t'} \right) = {\left( {2\pi } \right)^{ - ... ..._T {\gamma \left( t \right)} \exp \left( {i\omega \cdot t} \right)dt d\omega } $

as well as a more general one wherein the Fourier kernels are weighted. When $ \Omega $ and $ T$ are $ N$-dimensional spherical domains, the eigenfunctions of the integral equation are generalized prolate spheroidal functions for which a new nomenclature is proposed. Many properties of the eigenfunctions are developed and summarized. Because of the importance of these functions in Fourier transform theory, old as well as new properties are included.

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DOI: https://doi.org/10.1090/qam/422988
Article copyright: © Copyright 1972 American Mathematical Society

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