(Lecture Jun 15) Growth of $L^/infty$-norm of Thue-Morse Polynomials and Ergodic Optimization
2018-06-13 readCount:76
Topic: Growth of $L^/infty$-norm of Thue-Morse Polynomials and Ergodic Optimization
Speaker: Pro. Aihua Fan(Central China Normal University & University of Amiens)
Venue: Room 318, Buliding No.4, Wushan Campus
Time: Friday, Jun 15, 2018, 15:00-16:00
 
[Abstract]
Thue-Morse sequence and its generalizations, which are all $2$-multiplicative, define what we call Thue-Morse (trigonometric) polynomials. Such $2$-multiplicativity (and more general $q$-multiplicativity) was introduced by A.O. Gelfond who were interested in number theory. The estimates of $L^p$-norms are problems to be solved and few results exist.We study the $L^/infty$-norm from the point of view of dynamical systems.Here the angle-doubling system is involved. We prove that the $L^/infty$-norm grows polynomially like $O(N^/gamma)$ and the best exponent $/gamma$ is simply related to the maximum value of a dynamical maximization, which is attained by a Sturmian measure. This is a part of joint work with Joerg Schmeling and Wexiao Shen. Furthermore, it can be proved that Thue-Morse sequence and its generalizations are all Gowers uniform of all orders. This is a joint work with Jakub Konieczny.
 
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Announced by School of Mathematics