Synopses & Reviews
The book begins with an exposition of Hardy spaces of slit domains and then proceeds to several descriptions of the invariant subspaces of the operator multiplication by z. Along the way, we discuss and characterize the nearly invariant subspaces of these Hardy spaces and examine conditions for z-invariant subspaces to be cyclic. This work also makes important connections to model spaces for the standard backward shift operator as well as the de Branges spaces of entire functions. The book is written for a graduate student or professional with a reasonable knowledge of Hardy spaces of the disk and basic complex and functional analysis.
Review
From the reviews: "This memoir is concerned with the description of the shift-invariant subspaces of a Hardy space on a slit domain ... . this brief monograph represents an interesting and valuable contribution to the literature on the subject of shift-invariant subspaces. It should be helpful for researchers and advanced graduate students specializing in the field." (Dragan Vukotić, Mathematical Reviews, Issue 2011 m)
Synopsis
This book examines Hardy spaces of slit domains and offers several descriptions of the invariant subspaces of the operator multiplication by z. It also discusses and characterizes the nearly invariant subspaces of these Hardy spaces.
Table of Contents
Preface; Notation; List of Symbols; Preamble; 1 Introduction; 2 Preliminaries; 3 Nearly invariant subspaces; 4 Nearly invariant and the backward shift; 5 Nearly invariant and de Branges spaces; 6 Invariant subspaces of the slit disk; 7 Cyclic invariant subspaces; 8 The essential spectrum; 9 Other applications; 10 Domains with several slits; 11 Final thoughts; 12 Appendix