Poisson summation formula
From Encyclopedia of Mathematics
The formula
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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
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where and
are any two positive numbers satisfying the condition
, and
is the Fourier transform of the function
:
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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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Poisson_summation_formula&oldid=13421
Poisson summation formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Poisson_summation_formula&oldid=13421
This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article