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An Introduction to the Uncertainty Principle by Sundaram Thangavelu
An Introduction to the Uncertainty Principle by Sundaram Thangavelu
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An Introduction to the Uncertainty Principle

Hardy’s Theorem on Lie Groups
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Description

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer­ sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo­ pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.
Release date NZ
October 12th, 2012
Audience
  • Professional & Vocational
Edition
Softcover reprint of the original 1st ed. 2004
Illustrations
XIII, 174 p.
Pages
174
Dimensions
156x234x10
ISBN-13
9781461264682
Product ID
21268295

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