The Resource Seminar on singularities of solutions of linear partial differential equations, edited by Lars Hörmander
Seminar on singularities of solutions of linear partial differential equations, edited by Lars Hörmander
 Summary
 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 19771978. 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 nonspecialist
 Language
 eng
 Extent
 1 online resource.
 Contents

 Cover; Title; Copyright; CONTENTS; PREFACE; SPECTRAL ANALYSIS OF SINGULARITIES; 1. Introduction; 2. Definition and basic properties of the singular spectrum; 3. The noncharacteristic regularity theorem; 4. Pseudodifferential operators; 5. Bicharacteristics and symplectic geometry; 6. Fourier integral operators corresponding to canonical transformations; 7. Further equivalence theorems; 8. Propagation of singularities and semiglobal existence theorems for pseudodifferential 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 pseudodifferential 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. Pseudodifferential operators; 5. Fourier integral operators; 6 . Normal forms; 7. Other boundary conditions
 8. Higherorder 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. Weyltype formulas; 3. Szegötype formulas I; 4. Szegötype formulas II; A SZEGÖ THEOREM AND COMPLETE SYMBOLIC CALCULUS FOR PSEUDODIFFERENTIAL OPERATORS; 1. Introduction; 2. Pseudodifferential families in Rn̂; 3. The halfspace problem
 4. Pseudodifferential operators on manifolds5. The heat expansion; 6. Functional calculus
 Isbn
 9781400881581
 Label
 Seminar on singularities of solutions of linear partial differential equations
 Title
 Seminar on singularities of solutions of linear partial differential equations
 Statement of responsibility
 edited by Lars Hörmander
 Language
 eng
 Summary
 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 19771978. 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 nonspecialist
 Cataloging source
 YDXCP
 Illustrations
 illustrations
 Index
 no index present
 Language note
 In English
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Annals of mathematics studies
 Series volume
 no. 91
 Label
 Seminar on singularities of solutions of linear partial differential equations, edited by Lars Hörmander
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents

 Cover; Title; Copyright; CONTENTS; PREFACE; SPECTRAL ANALYSIS OF SINGULARITIES; 1. Introduction; 2. Definition and basic properties of the singular spectrum; 3. The noncharacteristic regularity theorem; 4. Pseudodifferential operators; 5. Bicharacteristics and symplectic geometry; 6. Fourier integral operators corresponding to canonical transformations; 7. Further equivalence theorems; 8. Propagation of singularities and semiglobal existence theorems for pseudodifferential 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 pseudodifferential 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. Pseudodifferential operators; 5. Fourier integral operators; 6 . Normal forms; 7. Other boundary conditions
 8. Higherorder 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. Weyltype formulas; 3. Szegötype formulas I; 4. Szegötype formulas II; A SZEGÖ THEOREM AND COMPLETE SYMBOLIC CALCULUS FOR PSEUDODIFFERENTIAL OPERATORS; 1. Introduction; 2. Pseudodifferential families in Rn̂; 3. The halfspace problem
 4. Pseudodifferential operators on manifolds5. The heat expansion; 6. Functional calculus
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