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El. knyga: Introduction To Pseudo-differential Operators, An (3rd Edition)

(York Univ, Canada)
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The aim of this third edition is to give an accessible and essentially self-contained account of pseudo-differential operators based on the previous edition. New chapters notwithstanding, the elementary and detailed style of earlier editions is maintained in order to appeal to the largest possible group of readers. The focus of this book is on the global theory of elliptic pseudo-differential operators on Lp(Rn).The main prerequisite for a complete understanding of the book is a basic course in functional analysis up to the level of compact operators. It is an ideal introduction for graduate students in mathematics and mathematicians who aspire to do research in pseudo-differential operators and related topics.
Preface v
1 Introduction, Notation and Preliminaries
1(4)
2 Differentiation of Integrals Depending on Parameters
5(4)
3 The Convolution
9(8)
4 The Fourier Transform
17(10)
5 Tempered Distributions
27(4)
6 Symbols, Pseudo-Differential Operators and Asymptotic Expansions
31(12)
7 A Partition of Unity and Taylor's Formula
43(12)
8 The Product of Two Pseudo-Differential Operators
55(6)
9 The Formal Adjoint of a Pseudo-Differential Operator
61(8)
10 The Parametrix of an Elliptic Pseudo-Differential Operator
69(6)
11 Lp-Boundedness of Pseudo-Differential Operators
75(12)
12 The Sobolev Spaces Hs,p, --∞ < s < ∞, 1 ≤ p < ∞
87(8)
13 Closed Linear Operators
95(4)
14 Minimal and Maximal Pseudo-Differential Operators
99(6)
15 Global Regularity of Elliptic Partial Differential Equations
105(4)
16 Weak Solutions of Pseudo-Differential Equations
109(4)
17 Gårding's Inequality
113(8)
18 Strong Solutions of Pseudo-Differential Equations
121(8)
19 One-Parameter Semigroups Generated by Pseudo-Differential Operators
129(14)
20 Fredholm Operators
143(12)
21 Fredholm Pseudo-Differential Operators
155(12)
22 Symmetrically Global Pseudo-Differential Operators
167(10)
23 Spectral Invariance of Symmetrically Global Pseudo-Differential Operators
177(4)
Bibliography 181(2)
Index 183