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The theory of H(b) spaces. Volume 1
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Description
Rating
Title
The
theory
of
H(b)
spaces
.
Volume
1
Creator
Fricain, Emmanuel, 1971
Mashreghi, Javad
DescriptionAbstract
An
H(b)
space
is
defined
as a
collection
of
analytic
functions
which
are in the
image
of an
operator
. The
theory
of
H(b)
spaces
bridges
two
classical
subjects
:
complex
analysis
and
operator
theory
,
which
makes
it
both
appealing
and
demanding
. The
first
volume
of this
comprehensive
treatment
is
devoted
to the
preliminary
subjects
required
to
understand
the
foundation
of
H(b)
spaces
,
such
as
Hardy
spaces
,
Fourier
analysis
,
integral
representation
theorems
,
Carleson
measures
,
Toeplitz
and
Hankel
operators
,
various
types
of
shift
operators
, and
Clark
measures
. The
second
volume
focuses
on the
central
theory
.
Both
books
are
accessible
to
graduate
students
as
well
as
researchers
:
each
volume
contains
numerous
exercises
and
hints
, and
figures
are
included
throughout
to
illustrate
the
theory
.
Together
, these
two
volumes
provide
everything
the
reader
needs
to
understand
and
appreciate
this
beautiful
branch
of
mathematics
.
DescriptionTable Of Contents
Machine
generated
contents
note
:
List
of
figures
;
Preface
;
List
of
symbols
;
Important
conventions
;
1
.
*Normed
linear
spaces
and their
operators
;
2
.
Some
families
of
operators
;
3
.
Harmonic
functions
on the
open
unit
disc
;
4
.
Analytic
functions
on the
open
unit
disc
;
5
. The
corona
problem
;
6
.
Extreme
and
exposed
points
;
7
.
More
advanced
results
in
operator
theory
;
8
. The
shift
operator
;
9
.
Analytic
reproducing
kernel
Hilbert
spaces
;
10
.
Bases
in
Banach
spaces
;
11
.
Hankel
operators
;
12
.
Toeplitz
operators
;
13
.
Cauchy
transform
and
Clark
measures
;
14
.
Model
subspaces
KT
;
15
.
Bases
of
reproducing
kernels
and
interpolation
;
Bibliography
;
Index
.
Publisher
Cambridge University Press
Subject
Hilbert space
Hardy spaces
Analytic functions
Linear operators
Identifier (Full text)
https://doi.org/10.1017/CBO9781139226752
ISBN
9781139226752
(ebook)
;
9781107027770
(hardback)
Language
eng
Type
Text
FormatExtent
1 online resource (xix, 681 p.)
Date
2016
RelationIs Part Of
New mathematical monographs
20
Purchased by
Puey Ungphakorn Library, Rangsit Campus
OCLC number
1017744832
CONTENTdm number
17282
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