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E-raamat: Functional Analysis in Applied Mathematics and Engineering

(Technical University of Denmark, Lyngby, Denmark)
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Functional Analysis in Applied Mathematics and EngineeringSuurem pilt
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Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering.

This text/reference discusses:

rudimentary topology

Banach's fixed point theorem with applications

L^p-spaces

density theorems for testfunctions

infinite dimensional spaces

bounded linear operators

Fourier series

open mapping and closed graph theorems

compact and differential operators

Hilbert-Schmidt operators

Volterra equations

Sobolev spaces

control theory and variational analysis

Hilbert Uniqueness Method

boundary element methods

Functional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.
Topological and Metric Spaces
1(10)
Some Topology
1(1)
Metric Spaces
2(9)
Banach Spaces
11(12)
Normed Vector Spaces
11(1)
Lp-spaces
12(7)
Infinite Dimensional Spaces
19(4)
Bounded Operators
23(10)
Basic Properties
23(3)
Bounded Linear Operators
26(7)
Hilbert Spaces.
33(22)
Inner Product Spaces
33(3)
Hilbert Spaces
36(6)
Construction of Hilbert Spaces
42(7)
Orthogonal Projection and Complement
49(3)
Weak Convergence
52(3)
Operators on Hilbert Spaces
55(22)
The Adjoint of a Bounded Operator
55(6)
Compactness and Compact Operators
61(4)
Closed Operators
65(8)
The Adjoint of an Unbounded Operator
73(4)
Spectral Theory
77(14)
The Spectrum and the Resolvent
78(8)
Operator-Valued Functions
86(5)
Integral Operators
91(10)
Introduction
91(1)
The Class of Hilbert-Schmidt Operators
92(6)
Integral Equations
98(3)
Semigroups of Evolution
101(10)
Strongly Continuous Semigroups
101(7)
The Resolvent
108(3)
Sobolev Spaces
111(16)
Basic Definitions
111(4)
Density Theorems
115(1)
Extension Theorems
116(1)
Imbedding Theorems
117(3)
Example
118(1)
Applications
119(1)
Example
119(1)
The Trade Theorem
120(4)
Negative Sobolev Spaces and Duality
124(3)
Interpolation Spaces
127(14)
Intermediate and Interpolation Spaces
127(2)
The Operator L
128(1)
Intermediate Derivatives Theorem
129(4)
An Example
131(1)
A Continuity Property
132(1)
Interpolation Theorem
133(4)
Reiteration Properties
135(1)
Duality
136(1)
Interpolation
137(1)
Interpolation with Hilbert Range
138(3)
The Space Lp(0, T; X)
138(1)
Distributions on ]0, T[ with Values in X
139(1)
Interpolation between Lp (0, T; H) Spaces
139(2)
Linear Elliptic Operators
141(32)
Elliptic Operators
142(1)
The Dirichlet Problem, Types of Solutions
143(2)
Boundary Operators
145(4)
Elliptic Equations
146(1)
The Formal Adjoint of A
147(1)
A Modified Version of Green's Formula
148(1)
V-elliptic and V-coercive Forms
149(4)
The Boundary Conditions
153(3)
Realization of the Operator A
153(2)
The V-space
155(1)
Variational Formulation
156(2)
Assumptions for the Variational Problem
158(1)
A Classical Regularity Result
159(10)
A Regularity Theorem
159(9)
An Abstract Regularity Theorem
168(1)
Transposition
169(4)
Transposition of Nonhomogeneous Boundary Value Problems
171(2)
Regularity of Hyperbolic Mixed Problems
173(36)
Solvability Results
174(8)
Classical Solvability Results
174(4)
Newer Solvability Theorems
178(2)
A Discussion of the Regularity Results
180(2)
Proofs of the Newer Regularity Theorems
182(16)
Proofs of Theorems from 12.1.2
191(7)
Interpolation Results
198(2)
Some Additional Regularity Theorems
200(1)
Systems with Variable Coefficients
201(8)
A Regularity Theorem
201(8)
The Hilbert Uniqueness Method
209(35)
Dirichlet Boundary Control
210(17)
Application of HUM
210(3)
Preliminary Lemmas
213(10)
A Discussion of the Control Area
223(1)
Exact Controllability in Polygons and Polyhedra
224(3)
The Hilbert Uniqueness Method
227(6)
The Problem of Exact Controllability
228(1)
The Operator Λ
229(4)
The Variable Coefficients Case
233(11)
Notation and Properties of the Operator A
233(1)
Preliminary Lemmas
234(2)
Application of HUM
236(8)
Exercises 244(47)
References 291


Pedersen\, Michael
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
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