The Cauchy problem and pseudodifferential operators in the complex domain

Abstract

CONTENTS Preface Chapter I. The analytic theory Introduction § 1. The Cauchy problem in spaces (the case of cylindrical evolution) § 2. The Cauchy problem in spaces (the case of conical evolution) § 3. The adjoint problem Chapter II. The exponential theory Introduction § 1. The Cauchy problem in the scale § 2. The Cauchy problem in the scale § 3. The adjoint problem Chapter III. The connection between the analytic theory and the exponential theory Introduction § 1. Pseudodifferential operators with complex arguments § 2. The Cauchy problem for pseudodifferential equations § 3. Fourier transformation of analytic functions § 4. The fundamental diagram. Concluding section (the connection between the analytic and exponential theories) References