Seminar on singularities of solutions of linear partial differential equations /

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 th...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor Corporativo: Institute for Advanced Study (Princeton, N.J.)
Otros Autores: Hörmander, Lars
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 1979.
Colección:Annals of mathematics studies ; no. 91.
Temas:
Differential equations, Linear > Numerical solutions > Congresses.
Differential equations, Partial > Numerical solutions > Congresses.
Équations différentielles linéaires > Solutions numériques > Congrès.
Équations aux dérivées partielles > Solutions numériques > Congrès.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Differential equations, Linear > Numerical solutions
Differential equations, Partial > Numerical solutions
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover; Title; Copyright; CONTENTS; PREFACE; SPECTRAL ANALYSIS OF SINGULARITIES; 1. Introduction; 2. Definition and basic properties of the singular spectrum; 3. The non-characteristic regularity theorem; 4. Pseudo-differential operators; 5. Bicharacteristics and symplectic geometry; 6. Fourier integral operators corresponding to canonical transformations; 7. Further equivalence theorems; 8. Propagation of singularities and semi-global existence theorems for pseudo-differential operators satisfying condition (P); FOURIER INTEGRAL OPERATORS WITH COMPLEX PHASE FUNCTIONS; 0. Introduction.
  • 1. Local study2. Lagrangean manifolds associated to phase functions; 3. Global definition of Fourier integral distributions; 4. Fourier integral operators; 5. Application to the exponential of a pseudo-differential operator; HYPOELLIPTIC OPERATORS WITH DOUBLE CHARACTERISTICS; 1. Conditions for hypoellipticity; 2. The asymptotic behavior of the eigenvalues; DIFFERENTIAL BOUNDARY VALUE PROBLEMS OF PRINCIPAL TYPE; 1. Introduction; 2. Examples; 3. Symplectic geometry; 4. Pseudo-differential operators; 5. Fourier integral operators; 6 . Normal forms; 7. Other boundary conditions.
  • 8. Higher-order tangency9. Example (2.3) again; PROPAGATION OF SINGULARITIES FOR A CLASS OF OPERATORS WITH DOUBLE CHARACTERISTICS; 0. Introduction; 1. Statement of results; 2. Reduction to canonical form; 3. A simple example; 4. Results independent of the lower order terms; 5. Results depending on the lower order terms; SUBELLIPTIC OPERATORS; 1. Introduction; 2. The Taylor expansion of the principal symbol; 3. Necessary conditions for subellipticity; 4. Local properties of the principal symbol; 5. Estimates for the localized operators; 6. Proof of the sufficiency in Theorem 3.4.
  • 7. Calculus lemmas8. Concluding remarks; LACUNAS AND TRANSMISSIONS; 1. Sharp fronts; 2. Transmissions; 3. Boundary value problems; 4. Symmetry of the elementary solution of a hyperbolic equation; 5. Further developments; SOME CLASSICAL THEOREMS IN SPECTRAL THEORY REVISITED; 0. Introduction; 1. The lattice point problem; 2. Weyl-type formulas; 3. Szegö-type formulas I; 4. Szegö-type formulas II; A SZEGÖ THEOREM AND COMPLETE SYMBOLIC CALCULUS FOR PSEUDO-DIFFERENTIAL OPERATORS; 1. Introduction; 2. Pseudo-differential families in R^n; 3. The half-space problem.
  • 4. Pseudo-differential operators on manifolds5. The heat expansion; 6. Functional calculus.

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