Semigroups of Operators on Hardy Spaces and Cocycles of Holomorphic Flows

Abstract

In this paper the strongly continuous semigroups of bounded cocycleweighted composition operators for holomorphic flows on Hardy spaces are characterized. In the process, an easy-to-check criterion for an operator to be a weighted composition operator is established.

Weighted composition semigroups on some Banach spaces

“…Jafari, F., Slodkowski, Z. and Tonev, T. in [9] provided a characterization of strong continuity of weighted semigroups on the H p (1 ď p ă 8) through using abelian intertwiners of multiplication operator M z on H p . Motivated by their results, in this section, we consider the similar problem on the weighted Bergman space A p α for 1 ď p ă 8, ´1 ă α ă 8.…”

“…The other main result focuses on depicting strongly continuous semigroups of weighted composition operators on A p α (1 ď p ă 8, ´1 ă α ă 8), the weighted Bergman space with typical weight pα `1qp1 ´|z|q α . The method used here is motivated by the method given by Jafari, F., Slodkowski, Z. and Tonev, T. who provided a connection between weighted composition operators and abelian intertwiners of multiplication operator M z on H p (1 ď p ă 8) in [9].…”

On generators of C0-semigroups of composition operators

“…Seminal works in the context of Hardy spaces were [28] and [22] by the end of the eighties. More recently, in 2012, the authors of [20] studied which strongly continuous semigroups of operators on Banach spaces of analytic functions arise from holomorphic flows, where semigroups of weighted composition operators play an important role.…”

Coordinated Hyperspectral Imaging Nano-Satellite Networks for Space Situational Awareness

“…The reference section offers a complete list of the publications resulting from this project. The papers are organized as follows: (a) Papers ( [7], [13], [4], [12], [8]) are published in peer-reviewed journals ; (b) Papers ( [14], [15], [16], [17], [2], [1], [3], [10]) are published in non-peerreviewed journals or in conference proceedings; (c) There are no papers presented at meetings, but not published in conference proceedings; (d) Papers ( [18], [19], [5], [20], [11], [9]) are manuscripts submitted or in preparation, but not published; and (e) Papers ( [21], [22], [23]) are M.S. and Ph.D. theses resulting from the grant.…”