Asymptotics of operator and pseudo-differential equations

✍ Scribed by V.P. Maslov, V.E. Nazaikinskii

• Publisher: Springer
• Year: 1988
• Tongue: English
• Leaves: 319
• Series: Monographs in Contemporary Mathematics
• Category: Library

✦ Synopsis

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✦ Table of Contents

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Contents......Page 5
1. Examples and general statement of asymptotic problems for linear equations......Page 7
2. Quantization procedure and quantization conditions for general symplectic manifolds......Page 19
3. Feynman approach to operator calculus: its properties and advantages......Page 23
4. The outline of the book. Preliminary knowledge necessary to read this book. The section dependence scheme......Page 33
1. Introduction......Page 36
2. Functions of a single operator......Page 42
3. Functions of several operators......Page 84
4. Regular representations......Page 112
1. The canonical operator on a Lagrangian manifold in R^{2n}......Page 147
2. The canonical operator on a Lagrangian submanifold of a symplectic manifold......Page 186
3. The canonical sheaf on a symplectic 1R+-manifold......Page 199
4. Pseudo-differential operators and the Cauchy problem in the space F+(M)......Page 240
1. Equations with coefficients growing at infinity......Page 255
2. Poisson algebras and nonlinear commutation relations......Page 272
3. Poisson algebra with u-structure. Local considerations......Page 276
4. Symplectic manifold of a Poisson algebra and proof of the main theorem......Page 299
References......Page 316