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An Introduction to the Uncertainty Principle

Hardy s Theorem on Lie Groups

Language EnglishEnglish
Book Paperback
Book An Introduction to the Uncertainty Principle Sundaram Thangavelu
Libristo code: 06794796
Publishers Springer, Berlin, March 2013
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge... Full description
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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.

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About the book

Full name An Introduction to the Uncertainty Principle
Language English
Binding Book - Paperback
Date of issue 2013
Number of pages 174
EAN 9781461264682
ISBN 1461264685
Libristo code 06794796
Publishers Springer, Berlin
Weight 308
Dimensions 155 x 235 x 9
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