Download e-book for iPad: Almost Everywhere Convergence II. Proceedings of the by Alexanra Bellow, Alexandra Bellow, Roger L. Jones

By Alexanra Bellow, Alexandra Bellow, Roger L. Jones

ISBN-10: 0120855208

ISBN-13: 9780120855209

Virtually in all places Convergence II includes chosen papers shape the second one foreign convention on nearly all over the place convergence in likelihood and Ergodic idea, which happened on October 16-20, 1989 at Northwestern college. It includes survey papers and significant unique contributions and may attract researchers within the region of ergodic thought and harmonic research in addition to to graduate scholars coming into those fields of research

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Additional info for Almost Everywhere Convergence II. Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Evanston, Illinois, October 16–20, 1989

Example text

The helical transform can be used to compute the spectral measures of intervals. Combining formulas obtained by means of the functional calculus with the double maximal inequality for flows (strong (2, 2) for (7)), we can show that the spectral measure of a measure-preserving flow has a sort of continuity property at oo. This strengthens, for this case, Gaposhkin's necessary and sufficient spectral condition for a flow of unitary operators to satisfy the Local Ergodic Theorem [12]. THEOREM §. I2J: For a unitary flow {{]»: - o o < 5 < o o } on 12(Χ%%μ) with spectral measure £, /EL2(X,^B,/i), and any sequence rfc—>οο, the properties (i) and (ii) below are equivalent; if {U$} comes from a measurepreserving flow on X, then both properties hold: (i) £ ( - Γ έ , 0)Λ*) - .

E. even if f is an indicator function of a set of finite /i-measure (and hence belongs to all spaces Lp(/i) (1 < p < oo)). Moreover, we shall have h = 1 in our example. Let Ω = [0,1), and let μ be the Lebesgue measure on Ω. The flow is given by rtw = ω + t (with addition mod 1). The indicator function f = 1» will be constructed in a sequence of steps. ,n m such that sup l < m T n ,l * is large on Ω. Start with a large integer K = Kj. Define c = ix = 1/K, Let α > 0 be an irrational number. β = βχ = 1/K2.

Nat. Acad. Sei. A. 59 (1968), 349-353. 7. L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135-157. 8. M. Cotlar, A unified theory of Hubert transforms and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105-167. 9. H. Davenport and H. Halberstam, The values of a trigonometrical polynomial at well spaced points, Mathematika 13 (1966), 91-96. 10. C. Fefferman, On the convergence of multiple Fourier series, Bull. Amer. Math. Soc. 77 (1971), 744-745. 11.

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Almost Everywhere Convergence II. Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Evanston, Illinois, October 16–20, 1989 by Alexanra Bellow, Alexandra Bellow, Roger L. Jones


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