BibTeX
@MISC{Havin00onthe,
author = {V. P. Havin},
title = {On the Uncertainty Principle in Harmonic Analysis},
year = {2000}
}
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Abstract
The Uncertainty Principle (UP) as understood in this lecture is the following informal assertion: a non-zero “object” (a function, distribution, hyperfunc-tion) and its Fourier image cannot be too small simultaneously. “The smallness” is understood in a very broad sense meaning fast decay (at infinity or at a point, bilateral or unilateral), perforated (or bounded, or semibounded) support etc. The UP becomes a theorem for many “smallnesses ” and has a multitude of quite concrete quantitative forms. It plays a fundamental role as one of the major themes of classical Fourier analysis (and neighboring parts of analysis), but also in applications to physics and engineering. The lecture is a review of facts and techniques related to the UP; connec-tions with local and non-local shift invariant operators are discussed at the end of the lecture (including some topical problems of potential theory). The lecture is intended for the general audience acquainted with basic facts of Fourier analysis on the line and circle, and rudiments of complex analysis.
Keyphrases
uncertainty principle harmonic analysis topical problem general audience fundamental role support etc classical fourier analysis non-zero object major theme many smallness broad sense concrete quantitative form basic fact non-local shift invariant operator fourier image cannot fol-lowing informal assertion potential theory fourier analysis complex analysis
