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The backward shift on the Hardy space

Author: Joseph A Cima; William T Ross
Publisher: Providence, R.I. : American Mathematical Society, ©2000.
Series: Mathematical surveys and monographs, no. 79.
Edition/Format:   Print book : EnglishView all editions and formats
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  Read more...

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Document Type: Book
All Authors / Contributors: Joseph A Cima; William T Ross
ISBN: 0821820834 9780821820834
OCLC Number: 43607449
Description: xi, 199 pages ; 27 cm.
Contents: Classical boundary value results --
Limits --
Pseudocontinuations --
The Hardy space of the disk --
H[superscript p] and boundary values --
Fourier analysis and H[superscript p] theory --
The Cauchy transform --
Duality --
The Nevanlinna class --
The Hardy spaces of the upper-half plane --
Motivation --
Basic definitions --
Poisson and conjugate Poisson integrals --
Maximal functions --
The Hilbert transform --
Some examples --
The harmonic Hardy space --
Distributions --
The atomic decomposition --
Distributions and H[superscript p] --
The space H[superscript p] (C\R) --
The backward shift on H[superscript p] for p [set membership] (1, [infinity]) --
The case p] 1 --
The first and most straightforward proof --
The second proof --
using Fatou's jump theorem --
Application: Bergman spaces --
Application: spectral properties --
The third proof --
using the Nevanlinna theory --
Application: VMOA, BMOA, and L[superscript 1] [square root]H[superscript 1 subscript 0] --
The case p = 1 --
Cyclic vectors --
Duality --
The commutant --
Compactness of the inclusion operator --
The backward shift on H[superscript p] for p [set membership] (0, 1) --
The parameters --
A reduction --
Rational approximation --
Spectral properties --
Cyclic vectors --
Duality --
The commutant.
Series Title: Mathematical surveys and monographs, no. 79.
Responsibility: Joseph A. Cima, William T. Ross.

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