On Dualizing a Multivariable Poisson Summation Formula

Richard J. Duffin; Hans F. Weinberger

doi:10.1007/bf02648879

On Dualizing a Multivariable Poisson Summation Formula

Richard J. Duffin, Hans F. Weinberger

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function φ of one variable into a function and its cosine transform in a generalized sense. The present work presents conditions on φ for which the transform relation holds in the classical sense, and extends this result to a class of generalizations of the Poisson formula in any number of dimensions.

Original language	English (US)
Pages (from-to)	487-497
Number of pages	11
Journal	Journal of Fourier Analysis and Applications
Volume	3
Issue number	5
DOIs	https://doi.org/10.1007/bf02648879
State	Published - 1997

Keywords

Dual
Fourier transform
Poisson summation formula

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10.1007/bf02648879

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abstract = "It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function φ of one variable into a function and its cosine transform in a generalized sense. The present work presents conditions on φ for which the transform relation holds in the classical sense, and extends this result to a class of generalizations of the Poisson formula in any number of dimensions.",

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AU - Weinberger, Hans F.

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AB - It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function φ of one variable into a function and its cosine transform in a generalized sense. The present work presents conditions on φ for which the transform relation holds in the classical sense, and extends this result to a class of generalizations of the Poisson formula in any number of dimensions.

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KW - Fourier transform

KW - Poisson summation formula

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