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Poisson summation formula

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The formula

The Poisson summation formula holds if, for example, the function is absolutely integrable on the interval , has bounded variation and . The Poisson summation formula can also be written in the form

where and are any two positive numbers satisfying the condition , and is the Fourier transform of the function :

References

[1] A. Zygmund, "Trigonometric series" , 1–2 , Cambridge Univ. Press (1988)
[2] E.C. Titchmarsh, "Introduction to the theory of Fourier integrals" , Oxford Univ. Press (1948)
How to Cite This Entry:
Poisson summation formula. I.I. Volkov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Poisson_summation_formula&oldid=13421
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098