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Distributions and Operators
This book gives an introduction to distribution theory, in the spirit of Laurent Schwartz. 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 partial and ordinary differential equations. Her...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2009.
|
| Edición: | 1st ed. 2009. |
| Colección: | Graduate Texts in Mathematics,
252 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-0-387-84895-2 | ||
| 003 | DE-He213 | ||
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| 024 | 7 | |a 10.1007/978-0-387-84895-2 |2 doi | |
| 050 | 4 | |a QA319-329.9 | |
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| 100 | 1 | |a Grubb, Gerd. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Distributions and Operators |h [electronic resource] / |c by Gerd Grubb. |
| 250 | |a 1st ed. 2009. | ||
| 264 | 1 | |a New York, NY : |b Springer New York : |b Imprint: Springer, |c 2009. | |
| 300 | |a XII, 464 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Graduate Texts in Mathematics, |x 2197-5612 ; |v 252 | |
| 505 | 0 | |a 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. | |
| 520 | |a This book gives an introduction to distribution theory, in the spirit of Laurent Schwartz. 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 partial and ordinary differential equations. Here, the author provides an introduction to unbounded operators in Hilbert space, including a complete theory of extensions of operators, and applications using contraction semigroups. In more advanced parts of the book, the author shows how distribution theory is used to define pseudodifferential operators on manifolds, and gives a detailed introduction to the pseudodifferential boundary operator calculus initiated by Boutet de Monvel, which allows a modern treatment of elliptic boundary value problems. This book is aimed at graduate students, as well as researchers interested in its special topics, and as such, the author provides careful explanations along with complete proofs, and a bibliography of relevant books and papers. Each chapter has been enhanced with many exercises and examples. Unique topics include: * the interplay between distribution theory and concrete operators; * families of extensions of nonselfadjoint operators; * an illustration of the solution maps between distribution spaces by a fully worked out constant-coefficient case; * the pseudodifferential boundary operator calculus; * the Calderón projector and its applications. Gerd Grubb is Professor of Mathematics at University of Copenhagen. | ||
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 1 | 4 | |a Functional Analysis. |
| 650 | 2 | 4 | |a Differential Equations. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9780387849140 |
| 776 | 0 | 8 | |i Printed edition: |z 9781441927439 |
| 776 | 0 | 8 | |i Printed edition: |z 9780387848945 |
| 830 | 0 | |a Graduate Texts in Mathematics, |x 2197-5612 ; |v 252 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-0-387-84895-2 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||