Open AccessUNCERTAINTY PRINCIPLES FOR GROUPS AND RECONSTRUCTION OF SIGNALS
Author(s) -
S.Y. Novikov,
M.E. Fedina
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-6-102-109
Subject(s) - abelian group , mathematics , poisson summation formula , gaussian , poisson distribution , prime (order theory) , order (exchange) , pure mathematics , group (periodic table) , cyclic group , algebra over a field , mathematical analysis , combinatorics , statistics , fourier transform , chemistry , organic chemistry , physics , finance , quantum mechanics , economics
Uncertainty principles of harmonic analysis and their analogues for nite abelian groups are considered in the paper. Special attention is paid to the recent results of T. Tao and coauthors about cyclic groups of prime order. It is shown, that indicator functions of subgroups of nite Abelian groups are analogues of Gaussian functions. Finite-dimensional version of Poisson summation formula is proved. Opportunities of application of these results for reconstruction of discrete signals with incomplete number of coecients are suggested. The principle of partial isometric whereby we can determine the minimum number of measurements for stable recovery of the signal are formulated.