Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2003
|
| Schriftenreihe: | Progress in Mathematical Physics
26 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. A comprehensive bibliography and index round out the work. Key Topics: Part I: A brief introduction to (Schwartz) distribution theory; Elements from the theories of ultra distributions and hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties of and basic properties for distributions are developed with applications to constant coefficient ODEs and PDEs; the relation between distributions and holomorphic functions is developed as well. * Part II: Fundamental facts about Hilbert spaces and their geometry. The theory of linear (bounded and unbounded) operators is developed, focusing on results needed for the theory of Schr"dinger operators. The spectral theory for self-adjoint operators is given in some detail. * Part III: Treats the direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators, concludes with a discussion of the Hohenberg--Kohn variational principle. * Appendices: Proofs of more general and deeper results, including completions, metrizable Hausdorff locally convex topological vector spaces, Baire's theorem and its main consequences, bilinear functionals. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines |
| Beschreibung: | 1 Online-Ressource (XXIII, 471 p) |
| ISBN: | 9781461200499 9781461265894 |
| DOI: | 10.1007/978-1-4612-0049-9 |
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| spelling | Blanchard, Philippe Verfasser aut Mathematical Methods in Physics Distributions, Hilbert Space Operators, and Variational Methods by Philippe Blanchard, Erwin Brüning Boston, MA Birkhäuser Boston 2003 1 Online-Ressource (XXIII, 471 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematical Physics 26 Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. A comprehensive bibliography and index round out the work. Key Topics: Part I: A brief introduction to (Schwartz) distribution theory; Elements from the theories of ultra distributions and hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties of and basic properties for distributions are developed with applications to constant coefficient ODEs and PDEs; the relation between distributions and holomorphic functions is developed as well. * Part II: Fundamental facts about Hilbert spaces and their geometry. The theory of linear (bounded and unbounded) operators is developed, focusing on results needed for the theory of Schr"dinger operators. The spectral theory for self-adjoint operators is given in some detail. * Part III: Treats the direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators, concludes with a discussion of the Hohenberg--Kohn variational principle. * Appendices: Proofs of more general and deeper results, including completions, metrizable Hausdorff locally convex topological vector spaces, Baire's theorem and its main consequences, bilinear functionals. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines Mathematics Functional analysis Operator theory Mathematical optimization Mathematical physics Functional Analysis Operator Theory Optimization Mathematical Methods in Physics Mathematik Mathematische Physik Distributionstheorie (DE-588)4150254-1 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Linearer Operator (DE-588)4167721-3 s 1\p DE-604 Distributionstheorie (DE-588)4150254-1 s 2\p DE-604 Mathematische Physik (DE-588)4037952-8 s 3\p DE-604 Distribution Funktionalanalysis (DE-588)4070505-5 s 4\p DE-604 5\p DE-604 Brüning, Erwin Sonstige oth https://doi.org/10.1007/978-1-4612-0049-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Blanchard, Philippe Mathematical Methods in Physics Distributions, Hilbert Space Operators, and Variational Methods Mathematics Functional analysis Operator theory Mathematical optimization Mathematical physics Functional Analysis Operator Theory Optimization Mathematical Methods in Physics Mathematik Mathematische Physik Distributionstheorie (DE-588)4150254-1 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Hilbert-Raum (DE-588)4159850-7 gnd Linearer Operator (DE-588)4167721-3 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4150254-1 (DE-588)4070505-5 (DE-588)4159850-7 (DE-588)4167721-3 (DE-588)4037952-8 |
| title | Mathematical Methods in Physics Distributions, Hilbert Space Operators, and Variational Methods |
| title_auth | Mathematical Methods in Physics Distributions, Hilbert Space Operators, and Variational Methods |
| title_exact_search | Mathematical Methods in Physics Distributions, Hilbert Space Operators, and Variational Methods |
| title_full | Mathematical Methods in Physics Distributions, Hilbert Space Operators, and Variational Methods by Philippe Blanchard, Erwin Brüning |
| title_fullStr | Mathematical Methods in Physics Distributions, Hilbert Space Operators, and Variational Methods by Philippe Blanchard, Erwin Brüning |
| title_full_unstemmed | Mathematical Methods in Physics Distributions, Hilbert Space Operators, and Variational Methods by Philippe Blanchard, Erwin Brüning |
| title_short | Mathematical Methods in Physics |
| title_sort | mathematical methods in physics distributions hilbert space operators and variational methods |
| title_sub | Distributions, Hilbert Space Operators, and Variational Methods |
| topic | Mathematics Functional analysis Operator theory Mathematical optimization Mathematical physics Functional Analysis Operator Theory Optimization Mathematical Methods in Physics Mathematik Mathematische Physik Distributionstheorie (DE-588)4150254-1 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Hilbert-Raum (DE-588)4159850-7 gnd Linearer Operator (DE-588)4167721-3 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematics Functional analysis Operator theory Mathematical optimization Mathematical physics Functional Analysis Operator Theory Optimization Mathematical Methods in Physics Mathematik Mathematische Physik Distributionstheorie Distribution Funktionalanalysis Hilbert-Raum Linearer Operator |
| url | https://doi.org/10.1007/978-1-4612-0049-9 |
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