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Item Details
| Title:
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ON THE CONVERGENCE OF SYMBOL C KF(N KX)
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| By: |
Istvan Berkes, Michel Weber |
| Format: |
Paperback |
| List price:
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£61.00 |
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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: |
0821843249 |
| ISBN 13: |
9780821843246 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 September, 2009 |
| Edition: |
New ed. |
| Series: |
Memoirs of the American Mathematical Society 201, 943 |
| Pages: |
72 |
| Description: |
Presents a general study of the convergence problem and intends to prove several fresh results and improve a number of old results in the field. This title studies the case when the nk are random and investigates the discrepancy the sequence (nkx) mod 1. |
| Synopsis: |
Let f be a periodic measurable function and x (nk) an increasing sequence of positive integers. The authors study conditions under which the series k=1 Ckf(nkx)_ converges in mean and for almost every x. There is a wide classical literature on this problem going back to the 30's, but the results for general f are much less complete than in the trigonometric case f(x) = sin x. As it turns out, the convergence properties of k=1 ckf(nkx) in the general case are determined by a delicate interplay between the coefficient sequence (ck), the analytic properties of f and the growth speed and number-theoretic properties of (nk). In this paper the authors give a general study of this convergence problem, prove several new results and improve a number of old results in the field. They also study the case when the nk are random and investigate the discrepancy the sequence {nkx} mod 1. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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