Analysis: Part II Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis: Analysis, cartea 2
Autor Krzysztof Maurinen Limba Engleză Paperback – 30 noi 2001
| Toate formatele și edițiile | Preț | Express |
|---|---|---|
| Paperback (1) | 601.91 lei 39-44 zile | |
| SPRINGER NETHERLANDS – 30 noi 2001 | 601.91 lei 39-44 zile | |
| Hardback (2) | 891.95 lei 39-44 zile | |
| SPRINGER NETHERLANDS – 31 ian 1980 | 891.95 lei 39-44 zile | |
| SPRINGER NETHERLANDS – 31 aug 1976 | 1182.17 lei 6-8 săpt. |
Preț: 601.91 lei
Preț vechi: 752.38 lei
-20% Nou
Puncte Express: 903
Preț estimativ în valută:
106.51€ • 124.90$ • 93.54£
106.51€ • 124.90$ • 93.54£
Carte tipărită la comandă
Livrare economică 02-07 februarie 26
Preluare comenzi: 021 569.72.76
Specificații
ISBN-13: 9781402003141
ISBN-10: 1402003145
Pagini: 868
Dimensiuni: 155 x 235 x 46 mm
Greutate: 1.2 kg
Ediția:Softcover reprint of the original 1st ed. 1980
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Analysis
Locul publicării:Dordrecht, Netherlands
ISBN-10: 1402003145
Pagini: 868
Dimensiuni: 155 x 235 x 46 mm
Greutate: 1.2 kg
Ediția:Softcover reprint of the original 1st ed. 1980
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Analysis
Locul publicării:Dordrecht, Netherlands
V-ar putea interesa
-
-31%Preț: 490.71 lei710.44 lei -
Applied Functional Analysis: Applications to Mathematical PhysicsEberhard Zeidler-15%Preț: 683.72 lei804.37 lei -
A Short Course on Spectral TheoryWilliam Arveson-18%Preț: 901.02 lei1098.81 lei -
An Introduction to Banach Space TheoryRobert E. Megginson-15%Preț: 635.93 lei748.15 lei -
-27%Preț: 745.85 lei1021.72 lei -
User and Task Analysis for Interface DesignJoann T Hackos-20%Preț: 499.17 lei623.95 lei -
Wavelets – Theory & ApplicationsAK Louis-9%Preț: 1162.89 lei1277.90 lei -
Iterative Krylov Methods for Large Linear SystemsHenk A. van der Vorst-11%Preț: 450.87 lei506.59 lei -
Numerical RecipesWilliam H. Press-27%Preț: 763.80 lei1046.30 lei -
Optimization with PDE ConstraintsMichael Hinze-18%Preț: 862.81 lei1052.21 lei -
Introduction to Numerical AnalysisJ. Stoer-15%Preț: 583.43 lei686.38 lei -
Programming Finite Elements in Java™Gennadiy P. Nikishkov-15%Preț: 571.34 lei672.16 lei -
Vector CalculusPaul C. MatthewsPreț: 255.36 lei -
Complex AnalysisEberhard Freitag-15%Preț: 466.71 lei549.07 lei -
Nonlinear Solid MechanicsAdnan IbrahimbegovicPreț: 396.76 lei -
-15%Preț: 420.26 lei494.42 lei
Public țintă
ResearchDescriere
The
extraordinarily
rapid
advances
made
in
mathematics
since
World
War
II
have
resulted
in
analysis
becoming
an
enormous
organism
spread
ing
in
all
directions.
Gone
for
good
surely
are
the
days
of
the
great
French
"courses
of
analysis"
which
embodied
the
whole
of
the
"ana
lytical"
knowledge
of
the
times
in
three
volumes-as
the
classical
work
of
Camille
Jordan.
Perhaps
that
is
why
present-day
textbooks
of
anal
ysis
are
disproportionately
modest
relative
to
the
present
state
of
the
art.
More:
they
have
"retreated"
to
the
state
before
Jordan
and
Goursat.
In
recent
years
the
scene
has
been
changing
rapidly:
Jean
Dieudon
ne
is
offering
us
his
monumentel
Elements
d'Analyse
(10
volumes)
written
in
the
spirit
of
the
great
French
Course
d'Analyse.
To
the
best
of
my
knowledge,
the
present
book
is
the
only
one
of
its
size:
starting
from
scratch-from
rational
numbers,
to
be
precise-it
goes
on
to
the
theory
of
distributions,
direct
integrals,
analysis
on
com
plex
manifolds,
Kahler
manifolds,
the
theory
of
sheaves
and
vector
bun
dles,
etc.
My
objective
has
been
to
show
the
young
reader
the
beauty
and
wealth
of
the
unsual
world
of
modern
mathematical
analysis
and
to
show
that
it
has
its
roots
in
the
great
mathematics
of
the
19th
century
and
mathematical
physics.
I
do
know
that
the
young
mind
eagerly
drinks
in
beautiful
and
difficult
things,
rejoicing
in
the
fact
that
the
world
is
great
and
teeming
with
adventure.
Cuprins
XII.
Topology.
Uniform
Structures.
Function
Spaces.-
1.
Topological
Spaces.-
2.
A
Basis
of
Neighbourhoods.
Axioms
of
Countability.-
3.
Filters.-
4.
Compact
Spaces.-
5.
The
Cartesian
Product
of
Topological
Spaces.-
6.
Metric
Spaces.
Baire
Spaces.-
7.
The
Topological
Product
of
Metric
Spaces.-
8.
Semicontinuous
Functions.-
9.
Regular
Spaces.-
10.
Uniform
Spaces.
The
Completeness
of
a
Space.-
11.
Precompact
and
Compact
Uniform
Spaces.-
12.
Uniform
Structures
on
Spaces
of
Mappings.-
13.
Families
of
Equicontinuous
Mappings.
General
Ascoli
Theorem.-
14.
Complements
and
Exercises.-
XIII.
Theory
of
the
Integral.-
1.
Compactification
of
the
Real
Line.-
2.
The
Daniel—Stone
Integral.-
3.
The
Functional
?*
and
Its
Properties.-
4.
The
Outer
Measure.-
5.
Seminorms
Np.
The
Minkowski
and
Hölder
Inequalities.-
6.
The
Spaces
?p.-
7.
The
Spaces
?p.-
8.
The
Space
?1
of
Integrable
Functions.
The
Integral.-
9.
The
Set
?
for
the
Radon
Integral.
Semicontinuity.-
10.
Application
of
the
Lebesgue
Theorem.
Integrals
with
a
Parameter.
Integration
of
Series.-
11.
Measurable
Functions.-
12.
Measure.
Integrable
Sets.-
13.
The
Stone
Axiom
and
Its
Consequences.-
14.
The
Spaces
Lp.-
15.
The
Hahn-Banach
Theorem.-
16.
Hilbert
Spaces.
Theorem
on
Orthogonal
Decomposition.
The
General
Form
of
a
Linear
Functional.-
17.
The
Strong
Stone
Axiom
and
Its
Consequences.-
18.
The
Tensor
Product
of
Integrals.-
19.
The
Radon
Integral.
Stone’s
Second
Procedure.-
20.
Finite
Radon
Measures.
Tough
Measures.-
21.
The
Tensor
Product
of
Radon
Integrals.-
22.
The
Lebesgue
Integral
on
Rn.
Change
of
Variables.-
23.
Mapping
of
Radon
Integrals.-
24.
Integrals
with
Density.
The
Radon-Nikodym
Theorem.-
25.
The
Wiener
Integral.-
26.
The
Kolmogorov
Theorem.-
27.
Integration
of
Vector
Fields.-
28.
Direct
Integrals
of
Hilbert
Spaces.-
29.
On
the
Equivalence
of
the
Stone
and
Radon
Integral
Theories.-
30.
From
Measure
to
Integral.-
XIV.
Tensor
Analysis.
Harmonic
Forms.
Cohomology.
Applications
to
Electrodynamics.-
1.
Alternating
Maps.
Grassmann
Algebra.-
2.
Differential
Forms.-
3.
Cohomology
Spaces.
Poincaré
Lemma.-
4.
Integration
of
Differential
Forms.-
5.
Elements
of
Vector
Analysis.-
6.
The
Differentiate
Manifold.-
7.
Tangent
Spaces.-
8.
Covariant
Tensor
Fields.
Riemannian
Metric
and
Differential
Forms
on
a
Manifold.-
9.
Orientation
of
Manifolds.
Examples.-
10.
Poincaré—Stokes
Theorem
for
a
Manifold
with
Boundary.-
11.
Tensor
Densities.
Weyl
Duality.
Homology.-
12.
Weyl
Duality
and
Hodge
*operator.
Generalized
Green’s
formulas
on
Riemannian
Manifold.-
13.
Harmonic
Forms.
Hodge-Kodaira-de
Rham
Theory.-
14.
Application
to
Electrodynamics.-
15.
Invariant
Forms
(Hurwitz
Integral).
Cohomology
of
Compact
Lie
Groups.-
16.
Complements.
Exercises.-
XV.
Elementary
Properties
of
Holomorphic
Functions
of
Several
Variables.
Harmonic
Functions.-
1.
Holomorphic
Mappings.
Cauchy—Riemann
Equations.-
2.
Differential
Forms
on
Complex
Manifolds.
Forms
of
Type
(p,
q).
Operators
d?
and
d??.-
3.
Cauchy’s
Formula
and
its
Applications.-
4.
The
Topology
of
the
Space
of
Holomorphic
Functions
A(?).-
5.
Elementary
Properties
of
Harmonic
Functions.-
6.
Green’s
Function.
Poisson
Integral
Formula.
Harnack
Theorems..-
7.
Subharmonic
Functions.
Perron’s
Solution
of
the
Dirichlet
Proble.-
XVI.
Complex
Analysis
in
One
Dimension
(Riemann
Surfaces.-
1.
Zeros
of
Holomorphic
Functions
of
One
Variable.-
2.
Functions
Holomorphic
in
an
Annulus.
The
Laurent
Expansion.
Singularities.-
3.
Meromorphic
Functions.-
4.
Application
of
the
Calculus
of
Residues
to
the
Evaluation
of
Integrals.-
5.
Applications
of
the
Argument
Principle.-
6.
Functions
and
Differential
Forms
on
Riemann
Surfaces.-
7.
Analytic
Continuation.
Coverings.
Fundamental
Group.
The
Theory
of
Poincaré.-
8.
The
Koebe—Riemann
Theorem.
Non-Euclidean
Geometry.
Möbius
Transformations.-
9.
The
Perron
Method
for
Riemann
Surfaces.
The
Radó
Theorem.-
10.
Resolutive
Functions.
Harmonic
Measures.
Brelot’s
Theorem.-
11.
The
Green’s
Function
of
a
Riemann
Surface.-
12.
The
Uniformization
Theorem.-
13.
Runge’s
Theorem.
Theorem
of
Behnke
and
Stein.
Theorem
of
Malgrange.-
14.
Cousin
Problems
for
Open
Riemann
Surfaces.
Theorems
of
Mittag-Leffler
and
Weierstrass.-
15.
Examples
of
Partial
Fractions
and
Factorizations.
Functions
cos
?z,
?2/sin2
?z,
?(z).
Mellin
and
Hankel
Formulae.
Canonical
Products.-
16.
Elliptic
Functions.
Eisenstein
Series.
The
Function
?.-
17.
Modular
Functions
and
Forms.
The
Modular
Figure,
Discontinuous
Groups
of
Automorphisms.-
18.
The
Multiplicity
Formula
for
Zeros
of
a
Modular
Form.
Dimension
of
Vector
Spaces
M°(k,
?)
of
Cusp
Forms.-
19.
Mapping
Properties
of
j.
Picard
Theorem.
Elliptic
Curves.
Jacobi’s
Inversion
Problem.
Abel’s
Theorem.-
20.
Uniformization
Principle.
Automorphic
Forms.
Riemann—Roch
Theorem
and
Its
Consequences.
Historical
Sketch.-
21.
Appendices.
Exercises
(Proofs
of
Theorems
of
Runge,
Florack,
Koebe,
and
Hurwitz.
Triangle
Groups.
Elliptic
Integrals
and
Transcendental
Numbers).-
XVII.
Normal
and
Paracompact
Spaces.
Partition
of
Unity..-
1.
Locally
Compact
Spaces
Countable
at
Infinity.-
2.
Normal
Spaces.
Urysohn’s
Lemma.-
3.
Extendibility
of
Continuous
Functions
on
Normal
Spaces.-
4.
Tychonoff
Spaces.
Uniformizability.
Compactification.-
5.
The
Theory
of
Maximal
Ideals.-
6.
The
Gel’fand
Theory
of
Maximal
Ideals.-
7.
Connection
with
Quantum
Mechanics.-
8.
Locally
Finite
Families.-
9.
Paracompact
Spaces.
Partition
of
Unity.
Metric
Spaces
are
Paracompact.-
XVIII.
Measurable
Mappings.
The
Transport
of
a
Measure.
Convolutions
of
Measures
and
Functions.-
1.
Measurable
Mappings.-
2.
Topologies
Determined
by
Families
of
Mappings.-
3.
The
Transport
of
a
Measure.-
4.
The
Projective
Limits
of
Hausdorff
Spaces.
Infinite
Tensor
Products
and
the
Projective
Limits
of
Measures.-
5.
Convolutions
of
Measures
and
Functions.-
6.
Convolutions
of
Functions
and
Measures
on
Rp.-
7.
Convolutions
of
Integrable
Functions.-
XIX.
The
Theory
of
Distributions.
Harmonic
Analysis.-
1.
The
Space
C0?
(?).-
2.
A
Differentiate
Partition
of
Unity
on
Rn.-
3.
The
Space
of
Test
Functions.
Distributions.-
4.
Inductive
Limits.
The
Topology
of
the
Space
D.-
5.
The
Pasting
Together
Principle
for
Distributions.
The
Support
of
a
Distribution.-
6.
The
Space
e(?).
Distributions
with
Compact
Supports.-
7.
Operations
on
Distributions.-
8.
The
Convolution
Algebra
e
(Rn).-
9.
The
Image
of
a
Distribution.-
10.
Remarks
on
the
Tensor
Products
E??F
and
E??F.
The
Kernel
Theorem.-
11.
The
Tensor
Product
E
?
?F
of
Hilbert
Spaces.-
12.
Regularization
of
Distributions.-
13.
Examples
of
Distributions
Important
for
Applications.-
14.
The
Fourier
Transformation.
The
Space
l.-
15.
The
Fourier
Transformation
as
a
Unitary
Operator
on
the
Space
l2(Rn).-
16.
Tempered
Distributions.
The
Fourier
Transformation
in
l’.-
17.
The
Laplace-Fourier
Transformation
for
Functions
and
Distributions.
The
Paley-Wiener-Schwartz
Theorem.-
18.
Fundamental
Solutions
of
Differential
Operators.-
19.
Positive-Definite
Functions.
Positive
Distributions.
The
Theorems
of
Bochner
and
Minlos.-
20.
Representations
of
Locally
Compact
Groups.
The
Relation
between
Unitary
Representations
and
Positive-Definite
Functions.-
21.
The
Haar
Integral.-
Index
of
Symbols.-
Name
Index.