Function Spaces and Potential Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1996
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
314 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis. In particular, they play a decisive role in the modem theory of partial differential equations (PDE). Potential theory, which grew out of the theory of the electrostatic or gravitational potential, the Laplace equation, the Dirichlet problem, etc. , had a fundamental role in the development of functional analysis and the theory of Hilbert space. Later, potential theory was strongly influenced by functional analysis. More recently, ideas from potential theory have enriched the theory of those more general function spaces that appear naturally in the study of nonlinear partial differential equations. This book is motivated by the latter development. The connection between potential theory and the theory of Hilbert spaces can be traced back to C. F. Gauss [181], who proved (with modem rigor supplied almost a century later by O. Frostman [158]) the existence of equilibrium potentials by minimizing a quadratic integral, the energy. This theme is pervasive in the work of such mathematicians as D. Hilbert, Ch. -J. de La Vallee Poussin, M. Riesz, O. Frostman, A. Beurling, and the connection was made particularly clear in the work of H. Cartan [97] in the 1940's. In the thesis of J. Deny [119], and in the subsequent work of J. Deny and J. L. |
| Beschreibung: | 1 Online-Ressource (XI, 368 p) |
| ISBN: | 9783662032824 9783642081729 |
| DOI: | 10.1007/978-3-662-03282-4 |
Internformat
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| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |v 314 | |
| 500 | |a Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis. In particular, they play a decisive role in the modem theory of partial differential equations (PDE). Potential theory, which grew out of the theory of the electrostatic or gravitational potential, the Laplace equation, the Dirichlet problem, etc. , had a fundamental role in the development of functional analysis and the theory of Hilbert space. Later, potential theory was strongly influenced by functional analysis. More recently, ideas from potential theory have enriched the theory of those more general function spaces that appear naturally in the study of nonlinear partial differential equations. This book is motivated by the latter development. The connection between potential theory and the theory of Hilbert spaces can be traced back to C. F. Gauss [181], who proved (with modem rigor supplied almost a century later by O. Frostman [158]) the existence of equilibrium potentials by minimizing a quadratic integral, the energy. This theme is pervasive in the work of such mathematicians as D. Hilbert, Ch. -J. de La Vallee Poussin, M. Riesz, O. Frostman, A. Beurling, and the connection was made particularly clear in the work of H. Cartan [97] in the 1940's. In the thesis of J. Deny [119], and in the subsequent work of J. Deny and J. L. | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
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| institution | BVB |
| isbn | 9783662032824 9783642081729 |
| language | English |
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| spelling | Adams, David R. 1941- Verfasser (DE-588)115051058 aut Function Spaces and Potential Theory by David R. Adams, Lars Inge Hedberg Berlin, Heidelberg Springer Berlin Heidelberg 1996 1 Online-Ressource (XI, 368 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 314 Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis. In particular, they play a decisive role in the modem theory of partial differential equations (PDE). Potential theory, which grew out of the theory of the electrostatic or gravitational potential, the Laplace equation, the Dirichlet problem, etc. , had a fundamental role in the development of functional analysis and the theory of Hilbert space. Later, potential theory was strongly influenced by functional analysis. More recently, ideas from potential theory have enriched the theory of those more general function spaces that appear naturally in the study of nonlinear partial differential equations. This book is motivated by the latter development. The connection between potential theory and the theory of Hilbert spaces can be traced back to C. F. Gauss [181], who proved (with modem rigor supplied almost a century later by O. Frostman [158]) the existence of equilibrium potentials by minimizing a quadratic integral, the energy. This theme is pervasive in the work of such mathematicians as D. Hilbert, Ch. -J. de La Vallee Poussin, M. Riesz, O. Frostman, A. Beurling, and the connection was made particularly clear in the work of H. Cartan [97] in the 1940's. In the thesis of J. Deny [119], and in the subsequent work of J. Deny and J. L. Mathematics Functional analysis Potential theory (Mathematics) Potential Theory Functional Analysis Mathematik Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s Funktionenraum (DE-588)4134834-5 s 1\p DE-604 Hedberg, Lars Inge 1935-2005 Sonstige (DE-588)115051066 oth Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 314 (DE-604)BV049758308 314 https://doi.org/10.1007/978-3-662-03282-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Adams, David R. 1941- Function Spaces and Potential Theory Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics Mathematics Functional analysis Potential theory (Mathematics) Potential Theory Functional Analysis Mathematik Potenzialtheorie (DE-588)4046939-6 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4134834-5 |
| title | Function Spaces and Potential Theory |
| title_auth | Function Spaces and Potential Theory |
| title_exact_search | Function Spaces and Potential Theory |
| title_full | Function Spaces and Potential Theory by David R. Adams, Lars Inge Hedberg |
| title_fullStr | Function Spaces and Potential Theory by David R. Adams, Lars Inge Hedberg |
| title_full_unstemmed | Function Spaces and Potential Theory by David R. Adams, Lars Inge Hedberg |
| title_short | Function Spaces and Potential Theory |
| title_sort | function spaces and potential theory |
| topic | Mathematics Functional analysis Potential theory (Mathematics) Potential Theory Functional Analysis Mathematik Potenzialtheorie (DE-588)4046939-6 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Mathematics Functional analysis Potential theory (Mathematics) Potential Theory Functional Analysis Mathematik Potenzialtheorie Funktionenraum |
| url | https://doi.org/10.1007/978-3-662-03282-4 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT adamsdavidr functionspacesandpotentialtheory AT hedberglarsinge functionspacesandpotentialtheory |