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Item Details
| Title:
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AN INTRODUCTION TO THE UNCERTAINTY PRINCIPLE
HARDY'S THEOREM ON LIE GROUPS |
| By: |
Sundaram Thangavelu |
| Format: |
Paperback |
| List price:
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£93.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
1461264685 |
| ISBN 13: |
9781461264682 |
| Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
| Pub. date: |
12 October, 2012 |
| Series: |
Progress in Mathematics 217 |
| Pages: |
174 |
| Synopsis: |
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. |
| Illustrations: |
biography |
| Publication: |
US |
| Imprint: |
Springer-Verlag New York Inc. |
| Returns: |
Returnable |
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