Global Pseudo-differential Calculus on Euclidean Spaces

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Springer Science & Business Media, Jan 30, 2011 - Mathematics - 306 pages
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This book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators. The book includes classic calculus as a special case. It will be accessible to graduate students and of benefit to researchers in PDEs and mathematical physics.

 

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Contents

Introduction
1
Background Material
8
Chapter 1 Global PseudoDifferential Calculus
15
Chapter 2 ΓPseudoDifferential Operators and HPolynomials
67
Chapter 3 GPseudoDifferential Operators
129
Chapter 4 Spectral Theory
152
Chapter 5 NonCommutative Residue and Dixmier Trace
203
Chapter 6 Exponential Decay and Holomorphic Extension of Solutions
226
Bibliography
287
Index
301
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