Mathematics > Classical Analysis and ODEs
[Submitted on 23 Mar 2009]
Title:Orthonormal sequences in L^2(R^d) and time frequency localization
View PDFAbstract: We study uncertainty principles for orthonormal bases and sequences in L^2(\R^d). As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that there is no orthonormal basis for L^2(\R) for which the time and frequency means as well as the product of dispersions are uniformly bounded. The problem is related to recent results of J. Benedetto, A. Powell, and Ph. Jaming.
Our main tool is a time frequency localization inequality for orthonormal sequences in L^2(\R^d). It has various other applications.
Submission history
From: Eugenia Malinnikova [view email][v1] Mon, 23 Mar 2009 19:55:32 UTC (16 KB)
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