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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.

Mathematical analysis. --- Algebra. --- Abstract algebra. --- Algebraic Method. --- Algebraic analysis. --- Algebraic equation. --- Analytic continuation. --- Analytic function. --- Analytic manifold. --- Antiderivative. --- Associative property. --- Bochner's theorem. --- Boundary value problem. --- Cauchy problem. --- Cauchy's integral formula. --- Cauchy's integral theorem. --- Cauchy–Riemann equations. --- Characterization (mathematics). --- Cohomology. --- Commutative diagram. --- Commutative property. --- Compactification (mathematics). --- Complex conjugate. --- Complex manifold. --- Complexification (Lie group). --- Complexification. --- Computation. --- Contact geometry. --- Continuous function (set theory). --- Continuous function. --- Convex set. --- Cover (topology). --- David Hilbert. --- Diagram (category theory). --- Differential equation. --- Differential operator. --- Domain of a function. --- Elliptic partial differential equation. --- Epimorphism. --- Equation. --- Euler's formula. --- Exact sequence. --- Existential quantification. --- Fourier series. --- Fubini's theorem. --- Function (mathematics). --- Functional equation. --- Fundamental solution. --- Fundamental theorem. --- General linear group. --- Geometric transformation. --- Group homomorphism. --- Hamilton–Jacobi equation. --- Hausdorff space. --- Holomorphic function. --- Homeomorphism. --- Homomorphism. --- Hyperbolic partial differential equation. --- Hyperfunction. --- Initial value problem. --- Inner automorphism. --- Integral curve. --- Interval (mathematics). --- Lie derivative. --- Linear space (geometry). --- Mathematical induction. --- Mathematical physics. --- Meromorphic function. --- Metric space. --- Monomorphism. --- Morphism. --- Nine lemma. --- Open set. --- Operator (physics). --- Poisson bracket. --- Polar set. --- Polynomial. --- Power series. --- Presheaf (category theory). --- Principal bundle. --- Proper map. --- Quadratic form. --- Ring (mathematics). --- Series (mathematics). --- Set (mathematics). --- Sheaf (mathematics). --- Sign (mathematics). --- Singularity spectrum. --- Special case. --- Stein manifold. --- Submanifold. --- Subset. --- Support (mathematics). --- Symplectic manifold. --- Tensor product. --- Theorem. --- Topological space. --- Topology. --- Transversal (geometry). --- Variable (mathematics). --- Weierstrass preparation theorem. --- Zorn's lemma.