Ergodic Theory and its Connections with Harmonic Analysis: - download pdf or read online

By Karl E. Petersen, Ibrahim Salama

ISBN-10: 0521459990

ISBN-13: 9780521459990

This quantity includes articles that describe the connections among ergodic idea and convergence, pressure conception, and the speculation of joinings. those papers current the heritage of every sector of interplay, the main notable fresh effects, and the presently promising traces of analysis. within the mixture, they're going to offer an ideal advent for somebody starting learn in a single of those parts.

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Extra info for Ergodic Theory and its Connections with Harmonic Analysis: Proceedings of the 1993 Alexandria Conference

Sample text

12, we saw that if /3 = b/q E Xq then A(b/q) = 1 L e(n2blq) q n

This distinction between rational approximations with small denominators and with large ones is a fundamental feature of the so-called circle method to be discussed in more detail later . Let us denote Ut(/3) _ E e(n20) n2

Let A = (a,,,) a "block" sequence. This means that A is a union of intervals of consecutive integers: A = UIk f Z+, where (Ik) is a sequence of intervals in I[8+ . Show, using both the Fourier - analytic and the geometric method, that A is ergodic provided IIic I -> oo as k -* oo. JOSEPH M. 2. ,, F(t) = oo. a) Show that there is a strictly increasing sequence A of positive integers which is ergodic and satisfies t+00 F(t) = 0. ) b) Is there is a strictly increasing sequence A of positive integers which is ergodic and satisfies A(,) ?

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Ergodic Theory and its Connections with Harmonic Analysis: Proceedings of the 1993 Alexandria Conference by Karl E. Petersen, Ibrahim Salama


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