Elements of Functional Analysis: Graduate Texts in Mathematics, cartea 192
Traducere de S. Levy Autor Francis Hirsch, Gilles Lacombeen Limba Engleză Hardback – 25 mar 1999
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Specificații
ISBN-13: 9780387985244
ISBN-10: 0387985247
Pagini: 396
Dimensiuni: 155 x 235 x 24 mm
Greutate: 0.72 kg
Ediția:1999
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics
Locul publicării:New York, NY, United States
ISBN-10: 0387985247
Pagini: 396
Dimensiuni: 155 x 235 x 24 mm
Greutate: 0.72 kg
Ediția:1999
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics
Locul publicării:New York, NY, United States
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Public țintă
GraduateDescriere
This
book
arose
from
a
course
taught
for
several
years
at
the
Univer
sity
of
Evry-Val
d'Essonne.
It
is
meant
primarily
for
graduate
students
in
mathematics.
To
make
it
into
a
useful
tool,
appropriate
to
their
knowl
edge
level,
prerequisites
have
been
reduced
to
a
minimum:
essentially,
basic
concepts
of
topology
of
metric
spaces
and
in
particular
of
normed
spaces
(convergence
of
sequences,
continuity,
compactness,
completeness),
of
"ab
stract"
integration
theory
with
respect
to
a
measure
(especially
Lebesgue
measure),
and
of
differential
calculus
in
several
variables.
The
book
may
also
help
more
advanced
students
and
researchers
perfect
their
knowledge
of
certain
topics.
The
index
and
the
relative
independence
of
the
chapters
should
make
this
type
of
usage
easy.
The
important
role
played
by
exercises
is
one
of
the
distinguishing
fea
tures
of
this
work.
The
exercises
are
very
numerous
and
written
in
detail,
with
hints
that
should
allow
the
reader
to
overcome
any
difficulty.
Answers
that
do
not
appear
in
the
statements
are
collected
at
the
end
of
the
volume.
There
are
also
many
simple
application
exercises
to
test
the
reader's
understanding
of
the
text,
and
exercises
containing
examples
and
coun
terexamples,
applications
of
the
main
results
from
the
text,
or
digressions
to
introduce
new
concepts
and
present
important
applications.
Thus
the
text
and
the
exercises
are
intimately
connected
and
complement
each
other.
Cuprins
Prologue:
Sequences.-
1
Countability.-
2
Separability.-
3
The
Diagonal
Procedure.-
4
Bounded
Sequences
of
Continuous
Linear
Maps.-
I
Function
Spaces
and
Their
Duals.-
1
The
Space
of
Continuous
Functions
on
a
Compact
Set.-
1
Generalities.-
2
The
Stone—Weierstrass
Theorems.-
3
Ascoli’s
Theorem.-
2
Locally
Compact
Spaces
and
Radon
Measures.-
1
Locally
Compact
Spaces.-
2
Daniell’s
Theorem.-
3
Positive
Radon
Measures.-
3A
Positive
Radon
Measures
on
$${{\mathbb{R}}^{d}}$$
and
the
Stieltjes
Integral.-
3B
Surface
Measure
on
Spheres
in
$${{\mathbb{R}}^{d}}$$.-
4
Real
and
Complex
Radon
Measures.-
3
Hilbert
Spaces.-
1
Definitions,
Elementary
Properties,
Examples.-
2
The
Projection
Theorem.-
3
The
Riesz
Representation
Theorem.-
3A
Continuous
Linear
Operators
on
a
Hilbert
Space.-
3B
Weak
Convergence
in
a
Hilbert
Space.-
4
Hilbert
Bases.-
4
LpSpaces.-
1
Definitions
and
General
Properties.-
2
Duality.-
3
Convolution.-
II
Operators.-
5
Spectra.-
1
Operators
on
Banach
Spaces.-
2
Operators
in
Hilbert
Spaces.-
2A
Spectral
Properties
of
Hermitian
Operators.-
2B
Operational
Calculus
on
Hermitian
Operators.-
6
Compact
Operators.-
1
General
Properties.-
lA
Spectral
Properties
of
Compact
Operators.-
2
Compact
Selfadjoint
Operators.-
2A
Operational
Calculus
and
the
Fredholm
Equation.-
2B
Kernel
Operators.-
III
Distributions.-
7
Definitions
and
Examples.-
1
Test
Functions.-
lA
Notation.-
1B
Convergence
in
Function
Spaces.-
1C
Smoothing.-
1D
C?Partitions
of
Unity.-
2
Distributions.-
2A
Definitions.-
2B
First
Examples.-
2C
Restriction
and
Extension
of
a
Distribution
to
an
Open
Set.-
2D
Convergence
of
Sequences
of
Distributions.-
2E
Principal
Values.-
2F
Finite
Parts.-
3
Complements.-
3A
Distributions
of
Finite
Order.-
3B
The
Support
of
a
Distribution.-
3C
Distributions
with
Compact
Support.-
8
Multiplication
and
Differentiation.-
1
Multiplication.-
2
Differentiation.-
3
Fundamental
Solutions
of
a
Differential
Operator.-
3A
The
Laplacian.-
3B
The
Heat
Operator.-
3C
The
Cauchy-Riemann
Operator.-
9
Convolution
of
Distributions.-
1
Tensor
Product
of
Distributions.-
2
Convolution
of
Distributions.-
2A
Convolution
in
??.-
2B
Convolution
in
D?.-
2C
Convolution
of
a
Distribution
with
a
Function.-
3
Applications.-
3A
Primitives
and
Sobolev’s
Theorem.-
3B
Regularity.-
3C
Fundamental
Solutions
and
Partial
Differential
Equations.-
3D
The
Algebra
D+?.-
10
The
Laplacian
on
an
Open
Set.-
1
The
spaces
H1(?)
and
H01(?).-
2
The
Dirichlet
Problem.-
2A
The
Dirichlet
Problem.-
2B
The
Heat
Problem.-
2C
The
Wave
Problem.-
Answers
to
the
Exercises.
Caracteristici
Book
and
authors
are
well-known
from
the
original
edition
of
this
book
which
was
published
in
French
Authors include a truly unique assortment of well formulated and interesting exercises which test ones comprehension, as well as point out many related topics
Answers and hints are included, making it perfect for self-study
Authors include a truly unique assortment of well formulated and interesting exercises which test ones comprehension, as well as point out many related topics
Answers and hints are included, making it perfect for self-study