Hypo-Analytic Structures : Local Theory (PMS-40).

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In Hypo-Analytic Structures Franois Treves provides a systematic approach to the study of the differential structures on manifolds defined by systems of complex vector fields. Serving as his main examples are the elliptic complexes, among which the De Rham and Dolbeault are the best known, and the tangential Cauchy-Riemann operators. Basic geometric entities attached to those structures are isolated, such as maximally real submanifolds and orbits of the system. Treves discusses the existence, uniqueness, and approximation of local solutions to homogeneous and inhomogeneous equations.

Frontmatter -- Contents -- Preface -- I. Formally and Locally Integrable Structures. Basic Definitions -- II. Local Approximation and Representation in Locally Integrable Structures -- III. Hypo-Analytic Structures. Hypocomplex Manifolds -- IV. Integrable Formal Structures. Normal Forms -- V. Involutive Structures With Boundary -- VI. Local Integraboity and Local Solvability in Elliptic Structures -- VII. Examples of Nonintegrability and of Nonsolvability -- VIII. Necessary Conditions for the Vanishing of the Cohomology. Local Solvability of a Single Vector Field -- IX. FBI Transform in a Hypo-Analytic Manifold -- X. Involutive Systems of Nonlinear First-Order Differential Equations -- References -- Index.

In English.

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