Uncertainty principles for orthonormal sequences
نویسندگان
چکیده
منابع مشابه
Uncertainty principles for orthonormal sequences
The aim of this paper is to provide complementary quantitative extensions of two results of H.S. Shapiro on the time-frequency concentration of orthonormal sequences in L2(R). More precisely, Shapiro proved that if the elements of an orthonormal sequence and their Fourier transforms are all pointwise bounded by a fixed function in L2(R) then the sequence is finite. In a related result, Shapiro ...
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In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro. Finally, we show that Benedicks’ result implies that solutions of the Shrödinge...
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The aim of this paper is to provide complementary quantitative extensions of two results of H.S. Shapiro on the time-frequency concentration of orthonormal sequences in L(R). More precisely, Shapiro proved that if the elements of an orthonormal sequence and their Fourier transforms are all pointwise bounded by a fixed function in L(R) then the sequence is finite. In a related result, Shapiro al...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2007
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2006.09.001