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An Introduction to the Uncertainty Principle : Hardy's Theorem on Lie Groups. Softcover reprint of the original 1st ed. 2004.
・ISBN 978-1-4612-6468-2 paper EUR 99.99
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| 著者・編者 | Thangavelu, Sundaram, |
|---|---|
| シリーズ | Progress in Mathematics |
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2012 |
| ページ数 | 174 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-16916＞ |
解説
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.