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Hypo-Analytic Structures (PMS-40), Volume 40
François Treves
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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 and delimits their supports. The contents of this book consist of many results accumulated in the last decade by the author and his collaborators, but also include classical results, such as the Newlander-Nirenberg theorem. The reader will find an elementary description of the FBI transform, as well as examples of its use. Treves extends the main approximation and uniqueness results to first-order nonlinear equations by means of the Hamiltonian lift.
Originally published in 1993.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Kundenbewertungen
Submanifold, Jacobian matrix and determinant, Unit disk, Complex-analytic variety, Diagram (category theory), Support (mathematics), Complex manifold, Symplectic geometry, Hadamard three-circle theorem, Cohomology, Manifold, Mean value theorem, Vector field, Norm (mathematics), Ring homomorphism, Power series, Cauchy sequence, Multi-index notation, Coefficient, Complex number, Pullback, Pullback (category theory), Stokes' theorem, CR manifold, Identity matrix, De Rham cohomology, Dirac delta function, Integral equation, Differential form, Riemann mapping theorem, Exact differential, Theorem, Sesquilinear form, Analytic function, Eigenvalues and eigenvectors, Linear differential equation, F-space, Subset, Open set, Taylor series, Integer, Polynomial, Lipschitz continuity, Hypersurface, Monomial, Vector bundle, Corollary, Neighbourhood (mathematics), Projection (linear algebra), Algebra homomorphism, Holomorphic function, Cauchy problem, Basis (linear algebra), Pullback (differential geometry), Symplectic vector space, Open mapping theorem (complex analysis), Volume form, H-vector, Surjective function, Frobenius theorem (differential topology), Differential operator, Frobenius theorem (real division algebras), Sobolev space, Automorphism, Formal power series, Diffeomorphism, Equation, Existential quantification, Cauchy–Riemann equations, Riemann surface