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. 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