scholarly journals An uncertainty principle related to the Poisson summation formula

1996 ◽  
Vol 121 (1) ◽  
pp. 87-104 ◽  
Author(s):  
K. Gröchenig
Keyword(s):  
Uncertainty Principle ◽  
Summation Formula ◽  
Poisson Summation Formula ◽  
Poisson Summation

scholarly journals Uncertainty principles for the windowed offset linear canonical transform

2021 ◽  
Author(s):  
Wen-Biao Gao ◽  
Bing-Zhao Li
Keyword(s):  
Uncertainty Principle ◽  
Summation Formula ◽  
Poisson Summation Formula ◽  
Linear Canonical Transform ◽  
Uncertainty Principles ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Offset Linear Canonical Transform ◽  
Poisson Summation

The windowed offset linear canonical transform (WOLCT) can be identified as a generalization of the windowed linear canonical transform (WLCT). In this paper, we generalize several different uncertainty principles for the WOLCT, including Heisenberg uncertainty principle, Hardy’s uncertainty principle, Donoho–Stark’s uncertainty principle and Nazarov’s uncertainty principle. Finally, as application analogues of the Poisson summation formula and sampling formulas are given.

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).

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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