The backward shift on the Hardy space / Joseph A. Cima, William T. Ross.

Format:

Book

Author/Creator:

Cima, Joseph A., 1933- author.

Ross, William T., 1964- author.

Series:

Mathematical surveys and monographs ; no. 79.

Mathematical surveys and monographs ; volume 79

Language:

English

Subjects (All):

Hardy spaces.

Physical Description:

1 online resource (215 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2000]

Language Note:

English

Summary:

Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, "parts" of direct sums of the backward shift operator on the classical Hardy space H2 model certain types of contraction operators and potentially have connections to understanding the invariant subspaces of a general linear operator. This book is a thorough treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces H{p}. The characterization of the backward shift invariant subspaces of H{p} for 1

Contents:

""Contents""; ""Preface""; ""Numbering and notation""; ""Chapter 1. Overview""; ""Chapter 2. Classical boundary value results""; ""2.1. Limits""; ""2.2. Pseudocontinuations""; ""Chapter 3. The Hardy space of the disk""; ""3.1. Introduction""; ""3.2. H[sup(p)] and boundary values""; ""3.3. Fourier analysis and H[sup(p)] theory""; ""3.4. The Cauchy transform""; ""3.5. Duality""; ""3.6. The Nevanlinna class""; ""Chapter 4. The Hardy spaces of the upper-half plane""; ""4.1. Motivation""; ""4.2. Basic definitions""; ""4.3. Poisson and conjugate Poisson integrals""; ""4.4. Maximal functions""

""4.5. The Hilbert transform""""4.6. Some examples""; ""4.7. The harmonic Hardy space""; ""4.8. Distributions""; ""4.9. The atomic decomposition""; ""4.10. Distributions and H[sup(p)]""; ""4.11. The space H[sup(p)](C\R)""; ""Chapter 5. The backward shift on H[sup(p)] for ...""; ""5.1. The case p > 1""; ""5.2. The first and most straightforward proof""; ""5.3. The second proof - using Fatou's jump theorem""; ""5.4. Application: Bergman spaces""; ""5.5. Application: spectral properties""; ""5.6. The third proof - using the Nevanlinna theory""

""5.7. Application: VMOA, BMOA, and L[sup(1)]/H[sup(1)][sub(0)]""""5.8. The case p = 1""; ""5.9. Cyclic vectors""; ""5.10. Duality""; ""5.11. The commutant""; ""5.12. Compactness of the inclusion operator""; ""Chapter 6. The backward shift on H[sup(p)] for ...""; ""6.1. Introduction""; ""6.2. The parameters""; ""6.3. A reduction""; ""6.4. Rational approximation""; ""6.5. Spectral properties""; ""6.6. Cyclic vectors""; ""6.7. Duality""; ""6.8. The commutant""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""O""

""P""""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""X""; ""Y""; ""Z""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 191-194) and index.

Description based on print version record.

ISBN:

1-4704-1306-X