应365bet的邀请，美国佐治亚理工学院数学系Jeffrey S. Geronimo & Rafael de la Llave教授将于近日访问我院，并为我院师生作两场学术报告。
报告时间：6月23日 9:30—10:30
报告地点：理科楼202会议室
报告人： Prof. Jeffrey S. Geronimo
报告题目: Bivariate Fejer-Riesz Factorization
Abstract: In 1915 Fejer and Riesz showed that every positive trigonometric polynomial of degree n could be written as a magnitude squared of an algebraic polynomial of the same degree. This lemma has had many applications in signal processing, wavelets, and the trigonometric moment problem.I will review the one variable lemma and then present some results.
报告时间：6月24日 15:30—16:30
报告地点：理科楼202会议室
报告人：Prof. Rafael de la Llave
报告题目:Quasi-periodic and almost periodic solutions with infinite frequencies in lattice Hamiltonian systems
Abstract: We consider Hamiltonian coupled map lattices. We assume that in the uncoupled case，the dynamics at each site is such that it admits KAM tori and hyperbolic fixed points.Then, we show that, for small enough (essentially local) couplings we can get solutions which stay close to the hyperbolic fixed point for most sites, but there are some of them that stay close to the KAM tori of the system. The method of proof is by introducing some appropriate weights that campture the idea of locality and that satisfy good Banach algebra properties. Then we prove an a-posteriori theorem for tori with finite frequencies. Using the a-posteriori format, we can keep on adding frequencies and verify that there is a limiting solution.
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