The Calculation of Fourier Coefficients by the Mobius Inversion of the Poisson Summation Formula. Part I: Functions whose Early Derivatives are Continuous

1970 ◽  
Vol 24 (109) ◽  
pp. 101 ◽  
Author(s):  
J. N. Lyness
Keyword(s):  
Fourier Coefficients ◽  
Summation Formula ◽  
Poisson Summation Formula ◽  
Möbius Inversion ◽  
Poisson Summation

scholarly journals Some Finite Analogues of the Poisson Summation Formula

1961 ◽  
Vol 12 (3) ◽  
pp. 133-138 ◽  
Author(s):  
L. Carlitz
Keyword(s):  
Summation Formula ◽  
Poisson Summation Formula ◽  
Euler’S Constant ◽  
Image Position ◽  
Positive Integers ◽  
Euler's Constant ◽  
Poisson Summation

1. Guinand (2) has obtained finite identities of the typewhere m, n, N are positive integers and eitherorwhere γ is Euler's constant and the notation ∑′ indicates that when x is integral the term r = x is multiplied by ½. Clearly there is no loss of generality in taking N = 1 in (1.1).

A Poisson Summation Formula for Extensions of Number Fields

2000 ◽  
Vol 61 (1) ◽  
pp. 36-50
Author(s):  
Eduardo Friedman ◽  
Nils-Peter Skoruppa
Keyword(s):  
Summation Formula ◽  
Number Fields ◽  
Poisson Summation Formula ◽  
Poisson Summation

scholarly journals A strong version of Poisson summation

1997 ◽  
Vol 20 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Nelson Petulante
Keyword(s):  
Summation Formula ◽  
Poisson Summation Formula ◽  
Strong Version ◽  
Poisson Summation

We establish a generalized version of the classical Poisson summation formula. This formula incorporates a special feature called “compression”, whereby, at the same time that the formula equates a series to its Fourier dual, the compressive feature serves to enable both sides of the equation to converge.

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