Asymptotics of operator and pseudo-differential equations

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\0......Page 7
2. Quantization procedure and quantization conditions for general symplectic manifolds\0......Page 19
3. Feynman approach to operator calculus: its properties and advantages\0......Page 23
4. The outline of the book. Preliminary knowledge necessary to read this book. The section dependence scheme\0......Page 33
1. Introduction\0......Page 36
2. Functions of a single operator\0......Page 42
3. Functions of several operators\0......Page 84
4. Regular representations\0......Page 112
1. The canonical operator on a Lagrangian manifold in R^{2n}\0......Page 147
2. The canonical operator on a Lagrangian submanifold of a symplectic manifold\0......Page 186
3. The canonical sheaf on a symplectic 1R+-manifold\0......Page 199
4. Pseudo-differential operators and the Cauchy problem in the space F+(M)\0......Page 240
1. Equations with coefficients growing at infinity\0......Page 255
2. Poisson algebras and nonlinear commutation relations\0......Page 272
3. Poisson algebra with u-structure. Local considerations\0......Page 276
4. Symplectic manifold of a Poisson algebra and proof of the main theorem\0......Page 299
References\0......Page 316