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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

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
Contributor
Subject
Genre
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 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
Member of
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
Seminar on singularities of solutions of linear partial differential equations, edited by Lars Hörmander
Label
Seminar on singularities of solutions of linear partial differential equations, edited by Lars Hörmander
Link
http://www.jstor.org/stable/10.2307/j.ctt1bd6jvc
Publication
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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 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 Rn̂; 3. The half-space problem
  • 4. Pseudo-differential operators on manifolds5. The heat expansion; 6. Functional calculus
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{'f': 'http://opac.lib.rpi.edu/record=b4344157'}
Extent
1 online resource.
Form of item
online
Isbn
9781400881581
Media category
computer
Media MARC source
rdamedia
Media type code
c
Specific material designation
remote

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