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Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91

Lars Hörmander

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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

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.

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Schlagwörter

Elliptic boundary value problem, Asymptotic distribution, Differential operator, Ordinary differential equation, Riesz representation theorem, Adjoint equation, Projection (linear algebra), Spectral theorem, Trace class, Canonical transformation, Riemannian manifold, Partial differential equation, Variable (mathematics), Inclusion map, Asymptotic expansion, Continuous function (set theory), Pseudo-differential operator, Self-adjoint operator, Analytic continuation, Eigenfunction, Eigenvalues and eigenvectors, Characteristic function (probability theory), Dirichlet problem, Mathematical optimization, Oscillatory integral, Hyperbolic partial differential equation, Partition of unity, Holomorphic function, Toeplitz operator, Existence theorem, Calculus on manifolds, Trigonometric polynomial, Regularity theorem, Fundamental solution, Linear map, Polynomial, Characteristic equation, Differential equation, Integral transform, Hamiltonian vector field, Taylor series, Limit (mathematics), Equation, Fourier transform, Renormalization, Harmonic analysis, A priori estimate, Fourier inversion theorem, Poisson summation formula, Local diffeomorphism, Asymptotic formula, Exponential function, Laplace operator, Symplectic manifold, Functional calculus, Poisson bracket, Existential quantification, Symplectic geometry, Analytic function, Support (mathematics), Elementary proof, Spectral theory, Theorem, Riemann surface, Hilbert space, Analytic manifold, Fourier integral operator, Lagrangian (field theory), Sign (mathematics), Asymptotic analysis