# Poisson summation formula

From Encyclopedia of Mathematics

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