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Mathematical statistics --- Asymptotic theory --- Congresses

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Manifolds (Mathematics) --- Variétés (mathématiques) --- Symplectic manifolds --- Variétés symplectiques --- Équations aux dérivées partielles --- Differential equations, Partial --- Théorie asymptotique --- Asymptotic theory

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Asymptotic Analysis of Singular Perturbations

Differential equations --- Perturbation (Mathematics) --- Boundary layer. --- Asymptotic theory. --- Aerodynamics --- Fluid dynamics --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Mathematical physics --- 517.91 Differential equations --- Boundary layer --- Equations differentielles --- Perturbation (Mathématiques) --- Couche limite --- Asymptotic theory --- Théorie asymptotique --- ELSEVIER-B EPUB-LIV-FT --- 517.91 --- Numerical solutions --- Differential equations. --- Singular perturbations (Mathematics) --- Équations différentielles. --- Perturbations singulières (mathématiques) --- Theorie asymptotique

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Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.

Partial differential equations --- Differential equations, Linear --- Differential equations, Partial --- Equations différentielles linéaires --- Equations aux dérivées partielles --- Numerical solutions --- Congresses --- Solutions numériques --- Congrès --- Théorie asymptotique --- 517.95 --- -Differential equations, Partial --- -Partial differential equations --- Linear differential equations --- Linear systems --- Insect societies. --- Insects --- Congresses. --- Ecology. --- 517.95 Partial differential equations --- -517.95 Partial differential equations --- Equations différentielles linéaires --- Equations aux dérivées partielles --- Solutions numériques --- Congrès --- Théorie asymptotique --- -Hexapoda --- Insecta --- Pterygota --- Arthropoda --- Entomology --- Behavior, Animal --- Ecology --- Insecta. --- Insect societies --- Sociétés d'insectes --- Insectes --- Ecologie --- Numerical solutions&delete& --- Insects, Social --- Social insects --- Animal societies --- Behavior --- Insects. Springtails --- Animal ethology and ecology. Sociobiology --- Behavior, Animal. --- Équations aux dérivées partielles --- Solutions numériques. --- A priori estimate. --- Adjoint equation. --- Analytic continuation. --- Analytic function. --- Analytic manifold. --- Asymptote. --- Asymptotic analysis. --- Asymptotic distribution. --- Asymptotic expansion. --- Asymptotic formula. --- Big O notation. --- Calculus on manifolds. --- Canonical transformation. --- Characteristic equation. --- Characteristic function (probability theory). --- Codimension. --- Cohomology. --- Commutator. --- Complex manifold. --- Complex number. --- Continuous function (set theory). --- Continuous function. --- Covariant derivative. --- Diffeomorphism. --- Differential equation. --- Differential operator. --- Dirichlet problem. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Elementary proof. --- Elliptic boundary value problem. --- Equation. --- Equivalence class. --- Equivalence relation. --- Error term. --- Existence theorem. --- Existential quantification. --- Exponential function. --- Fourier integral operator. --- Fourier inversion theorem. --- Fourier transform. --- Functional calculus. --- Fundamental solution. --- Hamiltonian vector field. --- Hardy space. --- Harmonic analysis. --- Hermann Weyl. --- Hermitian adjoint. --- Hilbert space. --- Holomorphic function. --- Homogeneous function. --- Hyperbolic partial differential equation. --- Hyperfunction. --- Hypersurface. --- Inclusion map. --- Inequality (mathematics). --- Integer lattice. --- Integral transform. --- Irreducible representation. --- Lagrangian (field theory). --- Laplace operator. --- Limit (mathematics). --- Linear map. --- Local diffeomorphism. --- Manifold. --- Mathematical optimization. --- Maximal torus. --- Monotonic function. --- Ordinary differential equation. --- Oscillatory integral. --- Partial differential equation. --- Partition of unity. --- Poisson bracket. --- Poisson summation formula. --- Polynomial. --- Projection (linear algebra). --- Projective variety. --- Pseudo-differential operator. --- Regularity theorem. --- Renormalization. --- Riemann surface. --- Riemannian manifold. --- Riesz representation theorem. --- Self-adjoint operator. --- Self-adjoint. --- Sign (mathematics). --- Special case. --- Spectral theorem. --- Spectral theory. --- Summation. --- Support (mathematics). --- Symplectic geometry. --- Symplectic manifold. --- Taylor series. --- Theorem. --- Toeplitz operator. --- Trace class. --- Trigonometric polynomial. --- Unit disk. --- Variable (mathematics). --- Equations aux derivees partielles lineaires --- Équations aux dérivées partielles --- Solutions numériques.

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The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems.Originally published in 1979.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.

517.982.4 --- Pseudodifferential operators --- Operators, Pseudodifferential --- Pseudo-differential operators --- Theory of generalized functions (distributions) --- Pseudodifferential operators. --- 517.982.4 Theory of generalized functions (distributions) --- Operator theory --- Differential equations, Partial --- Équations aux dérivées partielles --- Opérateurs pseudo-différentiels --- Addition. --- Adjoint. --- Approximation. --- Asymptotic expansion. --- Banach space. --- Bounded operator. --- Boundedness. --- Calculation. --- Change of variables. --- Coefficient. --- Compact space. --- Complex analysis. --- Computation. --- Corollary. --- Cotangent bundle. --- Derivative. --- Differential operator. --- Disjoint union. --- Elliptic partial differential equation. --- Estimation. --- Euclidean distance. --- Euclidean vector. --- Existential quantification. --- Fourier integral operator. --- Fourier transform. --- Geometric series. --- Heat equation. --- Heisenberg group. --- Homogeneous distribution. --- Infimum and supremum. --- Integer. --- Integration by parts. --- Intermediate value theorem. --- Jacobian matrix and determinant. --- Left inverse. --- Linear combination. --- Linear map. --- Mean value theorem. --- Monograph. --- Monomial. --- Nilpotent group. --- Operator (physics). --- Operator norm. --- Order of magnitude. --- Orthogonal complement. --- Parametrix. --- Parity (mathematics). --- Partition of unity. --- Polynomial. --- Projection (linear algebra). --- Pseudo-differential operator. --- Quadratic function. --- Regularity theorem. --- Remainder. --- Requirement. --- Right inverse. --- Scientific notation. --- Self-reference. --- Several complex variables. --- Singular integral. --- Smoothness. --- Sobolev space. --- Special case. --- Submanifold. --- Subset. --- Sum of squares. --- Summation. --- Support (mathematics). --- Tangent space. --- Taylor's theorem. --- Theorem. --- Theory. --- Transpose. --- Triangle inequality. --- Uniform boundedness. --- Upper and lower bounds. --- Variable (mathematics). --- Without loss of generality. --- Zero set.