Grubb Distributions and Operators

1. Auflage 2008
ISBN: 978-0-387-84895-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 252, 476 Seiten, eBook

Reihe: Graduate Texts in Mathematics

This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. Additionally, the aim is to show how the theory is combined with the study of operators in Hilbert space by methods of functional analysis, with applications to ordinary and partial differential equations. In some of the latter chapters, the author illustrates how distribution theory is used to define pseudodifferential operators and how they are applied in the discussion of solvability of PDE, with or without boundary conditions. Each chapter has been enhanced with many exercises and examples, and a bibliography of relevant books and papers is collected at the end.

A few of the unique topics include: (1) Boundary value problems in a constant-coefficient case; (2) Pseudodifferential Boundary Operators; (3) Families of extensions.

Gerd Grubb is Professor of Mathematics at University of Copenhagen.

Zielgruppe

Graduate

Autoren/Hrsg.

Grubb, Gerd

Inhaltsverzeichnis

Distributions and derivatives.- Motivation and overview.- Function spaces and approximation.- Distributions. Examples and rules of calculus.- Extensions and applications.- Realizations and Sobolev spaces.- Fourier transformation of distributions.- Applications to differential operators. The Sobolev theorem.- Pseudodifferential operators.- Pseudodifferential operators on open sets.- Pseudodifferential operators on manifolds, index of elliptic operators.- Boundary value problems.- Boundary value problems in a constant-coefficient case.- Pseudodifferential boundary operators.- Pseudodifferential methods for boundary value problems.- Topics on Hilbert space operators.- Unbounded linear operators.- Families of extensions.- Semigroups of operators.