报告人简介：

刘锐，南开大学数学科学学院，教授/博导，研究方向：泛函分析空间理论及其应用，部分成果发表在Memoirs AMS, Advance Math., J. Funct. Anal., ACHA, Fund. Math., Sci. Math. China., Studia等期刊, 合作出版Springer专著一部。

报告简介：

Dynamical sampling focus on the signal recovery from the space-time samples from the orbits of evolution operators with window generators. One of the basic problems is to determine the semigroup representations, which we call central frame representations, whose frame window generators are unique (up to equivalence). Recently, Christensen, Hasannasab, and Philipp proved that all frame representations of the semigroup Z^+ have this property. Their proof relies on the characterization of the structure of shift-invariant subspaces in Hardy spaces due to Beurling. We settle the general uniqueness problem by presenting a characterization of central frame representations for any semigroup in terms of the hyperinvariant subspaces of the left regular representation of the semigroup. Our result proves that all the frame window generators of a semigroup generated by any k-tuple (A_1, ..., A_k) of commuting operators on Hilbert spaces are equivalent, a case where the structure of shift-invariant subspaces of the Hardy space H^2 on polydisks is still not completely characterized. (joint work with V. Bailey, D. Han, K. Kornelson, D. Larson).