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Technical Asymptotics of Operator and Pseudo-Differential Equations
Posted on 2010-08-20
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More V.P. Maslov, V.E. Nazaikinskii, "Asymptotics of Operator and Pseudo-Differential Equations" CHAPTER I INTRODUCTION 1 1. Examples and general statement of asymptotic problems for linear equations 1 2. Quantization procedure and quantization conditions for general symplectic manifolds 13 3. Feynman approach to operator calculus: its properties and advantages 17 4. The outline of the book. Preliminary knowledge necessary to read this book. The section dependence scheme 27 CHAPTER II FUNCTIONAL CALCULUS 30 1. Introduction 30 2. Functions of a single operator 36 3. Functions of several operators 78 4. Regular representations 106 CHAPTER III ASYMPTOTIC SOLUTIONS FOR PSEUDO-DIFFERENTIAL EQUATIONS 141 1. The canonical operator on a Lagrangian manifold in R^{2n} 141 2. The canonical operator on a Lagrangian submanifold of a symplectic manifold 180 3. The canonical sheaf on a symplectic 1R+-manifold 193 4. Pseudo-differential operators and the Cauchy problem in the space F+(M) 234 CHAPTER IV QUASI-INVERSION THEOREM FOR FUNCTIONS OF A TUPLE OF NON-COMMUTING OPERATORS 249 1. Equations with coefficients growing at infinity 249 2. Poisson algebras and nonlinear commutation relations 266 3. Poisson algebra with u-structure. Local considerations 270 4. Symplectic manifold of a Poisson algebra and proof of the main theorem 293 References 310 Download
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