| Distributions and Operators 2009 Edition Contributor(s): Grubb, Gerd (Author) |
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ISBN: 0387848940 ISBN-13: 9780387848945 Publisher: Springer OUR PRICE: $94.99 Product Type: Hardcover - Other Formats Published: October 2008 Annotation: 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: * Boundary value problems in a constant-coefficient case; * Pseudodifferential Boundary Operators; * families of extensions. Gerd Grubb is Professor of Mathematics at University of Copenhagen. |
| Additional Information |
| BISAC Categories: - Mathematics | Functional Analysis - Mathematics | Differential Equations - General - Mathematics | Calculus |
| Dewey: 515.782 |
| LCCN: 2008937582 |
| Series: Graduate Texts in Mathematics |
| Physical Information: 1.2" H x 6.4" W x 9.3" (1.80 lbs) 464 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This textbook gives an introduction to distribution theory with emphasis on applications using functional analysis. In more advanced parts of the book, pseudodi?erential methods are introduced. Distributiontheoryhasbeen developedprimarilytodealwithpartial(and ordinary) di?erential equations in general situations. Functional analysis in, say, Hilbert spaces has powerful tools to establish operators with good m- ping properties and invertibility properties. A combination of the two allows showing solvability of suitable concrete partial di?erential equations (PDE). When partial di?erential operators are realized as operators in L (?) for 2 n anopensubset?ofR, theycomeoutasunboundedoperators.Basiccourses infunctionalanalysisareoftenlimitedtothestudyofboundedoperators, but we here meet the necessityof treating suitable types ofunbounded operators; primarily those that are densely de?ned and closed. Moreover, the emphasis in functional analysis is often placed on selfadjoint or normal operators, for which beautiful results can be obtained by means of spectral theory, but the cases of interest in PDE include many nonselfadjoint operators, where diagonalizationbyspectraltheoryisnotveryuseful.Weincludeinthisbooka chapter on unbounded operatorsin Hilbert space (Chapter 12), where classes of convenient operators are set up, in particular the variational operators, including selfadjoint semibounded cases (e.g., the Friedrichs extension of a symmetric operator), but with a much wider scope. Whereas the functional analysis de?nition of the operators is relatively clean and simple, the interpretation to PDE is more messy and complicated. |