Generalized Weighted Composition Operators on Analytic Function Spaces

ISBN-13: 9783330088726 / Angielski / Miękka / 2017 / 152 str.

Xiangling Zhu

Opis

The study of composition operators and weighted composition operators lies at the interface of operator theory and function theory. Composition operators and weighted composition operators occur naturally in a variety of problems. Moreover, they are closely related to many famous problems, such as invariant subspace problem, Bieberbach's conjecture and Brennan's conjecture. This book is a collection of my recent published papers in area of "Generalized weighted composition operators on analytic function spaces". The book consists of five chapters, organized as follows. In chapter 1, we briefly recall the history of composition operators and weighted composition operators on some function spaces in the unit disk. In Chapter 2 we introduce some concepts used in this book. In Chapter 3 we study generalized weighted composition operators on Bloch type spaces. The differences of generalized weighted composition operators on Bloch type spaces are also investigated. In Chapter 4 we study generalized weighted composition operators on weighted Bergman spaces. In Chapter 5 we present some topics which require further research.

O autorze

Xiangling Zhu was born in P.R. China. Presently, she is an associate professor of Jiaying University. She is mainly interested in operator theory on analytic function spaces. She serves as a Reviewer of Mathematical Reviews of American Mathematical Society.