Leseprobe
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Foundations of Algebraic Analysis (PMS-37), Volume 37
Tatsuo Kimura, Takahiro Kawai, Masaki Kashiwara, et al.
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
The use of algebraic methods for studying analysts is an important theme in modern mathematics. The most significant development in this field is microlocal analysis, that is, the local study of differential equations on cotangent bundles. This treatise provides a thorough description of microlocal analysis starting from its foundations. The book begins with the definition of a hyperfunction. It then carefully develops the microfunction theory and its applications to differential equations and theoretical physics. It also provides a description of microdifferential equations, the microlocalization of linear differential equations. Finally, the authors present the structure theorems for systems of microdifferential equations, where the quantized contact transformations are used as a fundamental device.
The microfunction theory, together with the quantized contact transformation theory, constitutes a valuable new viewpoint in linear partial differential equations.
Originally published in 1986.
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
Nine lemma, Algebraic equation, Fubini's theorem, Linear space (geometry), Set (mathematics), Subset, Continuous function (set theory), General linear group, Interval (mathematics), Principal bundle, Topology, Commutative diagram, Metric space, Complexification (Lie group), Inner automorphism, Series (mathematics), Function (mathematics), Homomorphism, Algebraic Method, Fundamental theorem, Algebraic analysis, Complex manifold, Ring (mathematics), Differential operator, Submanifold, Weierstrass preparation theorem, Existential quantification, Analytic manifold, Holomorphic function, Bochner's theorem, Presheaf (category theory), Commutative property, Group homomorphism, Hamilton–Jacobi equation, Characterization (mathematics), Cohomology, Initial value problem, Sign (mathematics), Cauchy's integral theorem, Epimorphism, Topological space, Symplectic manifold, Hyperfunction, Hyperbolic partial differential equation, Sheaf (mathematics), Transversal (geometry), Open set, Variable (mathematics), Mathematical induction, Analytic continuation, Complexification, Exact sequence, Cauchy–Riemann equations, Compactification (mathematics), Diagram (category theory), Analytic function, Cover (topology), Contact geometry, Fundamental solution, Abstract algebra, Boundary value problem, Zorn's lemma, Operator (physics), Cauchy's integral formula, Functional equation, Theorem, Singularity spectrum, Support (mathematics), Equation, Euler's formula