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Poisson Summation Formulas and Inversion Theorems for an Infinite Continuous Legendre Transform

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Abstract

The classical Fourier transform and Fourier series are linked by the Poisson summation formula. The goal of this article is to find an infinite continuous Legendre transform which complements Legendre series in a similar way. To this end, the finite continuous Legendre transform due to Butzer/Stens/Wehrens is extended to an infinite transform. We show that for the new Legendre transform variants of Poisson’s formula and inversion theorems hold.

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  1. Zentrum Mathematik, Technische Universität München, Germany

    Roland Girgensohn

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  1. Roland Girgensohn
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Correspondence to Roland Girgensohn.

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Girgensohn, R. Poisson Summation Formulas and Inversion Theorems for an Infinite Continuous Legendre Transform. J Fourier Anal Appl 11, 151–173 (2005). https://doi.org/10.1007/s00041-005-3073-6

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  • DOI: https://doi.org/10.1007/s00041-005-3073-6

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