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 distributiontheory 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. First book to present distribution theory as a standard text Contains unique topics author has made this easily accessible to advanced undergraduates, as well as graduates INDICE: Preface.- Motivation and overview.- Function spaces and approximation.- Distributions: Examples and rules of calculus.- Realizations and Sobolevspaces.- Fourier transformation of distributions.- Applications to differential operators: The Sobolev theorem.- Pseudodifferential operators on open sets.- Pseudodifferential operators on manifolds, index of elliptic operators.- Boundary value problems in a constant-coefficient case.- Pseudodifferential boundary operators.- Pseudodifferential methods for boundary value problems.- Unbounded linear operators.- Families of extensions.- Semigroups of operators.- Some notation and prerequisites.- Topological vector spaces.- Function spaces on sets with smooth boundary.- Bibliography.- Index.
- ISBN: 978-0-387-84894-5
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 464
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés