An Introduction to the Uncertainty Principle : Hardy's Theorem on Lie Groups

Language: English

Published by Birkhäuser, 2012

1461264685 / 9781461264682

Series: Book 42 of 170 - Progress in Mathematics

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Druck auf Anfrage Neuware - Printed after ordering - 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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Title
An Introduction to the Uncertainty Principle : Hardy's Theorem on Lie Groups
Author
Sundaram Thangavelu
Publisher
Birkhäuser
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
1461264685
ISBN 13
9781461264682
Item weight
306 grams
Dimensions
235x155x11 mm
Series
Book 42 of 170: Progress in Mathematics

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