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目次

Chapter 1 Hyperfunctions > 1.1 Function spaces > 1.2 Supports > 1.3 Localization > 1.4 Hyperfunctions > 1.5 Further applications of the Runge approximation theorem >Chapter 2 Basic calculus of Fourier integral operators and pseudodifferential operators > 2.1 Preliminary lemmas > 2.2 Symbol classes > 2.3 Definition of Fourier integral operators > 2.4 Product formula of Fourier integral operators I > 2.5 Product formula of Fourier integral operators II > 2.6 Pseudolocal properties > 2.7 Pseudodifferential operators in B > 2.8 Parametrices of elliptic operators >Chapter 3 Analytic wave front sets and microfunctions > 3.1 Analytic wave front sets > 3.2 Action of Fourier integral operators on wave front sets > 3.3 The boundary values of analytic functions > 3.4 Operations on hyperfunctions > 3.5 Hyperfunctions supported by a half-space > 3.6 Microfunctions > 3.7 Formal analytic symbols >Chapter 4 Microlocal uniqueness > 4.1 Preliminary lemmas > 4.2 General results > 4.3 Microhyperbolic operators > 4.4 Canonical transformation > 4.5 Hypoellipticity >Chapter 5 Local solvability > 5.1 Preliminaries > 5.2 Necessary conditions on local solvability and hypoellipticity > 5.3 Sufficient conditions on local solvability > 5.4 Some examples >Chapter A Proofs of product formulae > A.1 Proof of Theorem 2.4.4 > A.2 Proof of Corollary 2.4.5 > A.3 Proof of Theorem 2.4.6 > A.4 Proof of Corollary 2.4.7 > A.5 Proof of Theorem 2.5.3 >Chapter B A priori estimates > B.1 Grusin operators > B.2 A class of operators with double characteristics