White Noise An Infinite Dimensional Calculus
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1993
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| Schriftenreihe: | Mathematics and Its Applications
253 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| 245 | 1 | 0 | |a White Noise |b An Infinite Dimensional Calculus |c by Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit |
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| 500 | |a Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in infinite dimensions based on white noise. By white noise we mean the generalized Gaussian process which is (informally) given by the time derivative of the Wiener process, i.e., by the velocity of Brownian mdtion. Therefore, in essence we present analysis on a Gaussian space, and applications to various areas of sClence. Calculus, analysis, and functional analysis in infinite dimensions (or dimension-free formulations of these parts of classical mathematics) have a long history. Early examples can be found in the works of Dirichlet, Euler, Hamilton, Lagrange, and Riemann on variational problems. At the beginning of this century, Frechet, Gateaux and Volterra made essential contributions to the calculus of functions over infinite dimensional spaces. The important and inspiring work of Wiener and Levy followed during the first half of this century. Moreover, the articles and books of Wiener and Levy had a view towards probability theory | ||
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Datensatz im Suchindex
| _version_ | 1819294260007010304 |
|---|---|
| any_adam_object | |
| author | Hida, Takeyuki |
| author_facet | Hida, Takeyuki |
| author_role | aut |
| author_sort | Hida, Takeyuki |
| author_variant | t h th |
| building | Verbundindex |
| bvnumber | BV042424329 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879623169 (DE-599)BVBBV042424329 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-3680-0 |
| format | Electronic eBook |
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| id | DE-604.BV042424329 |
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| indexdate | 2024-12-24T04:23:29Z |
| institution | BVB |
| isbn | 9789401736800 9789048142606 |
| language | English |
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| series2 | Mathematics and Its Applications |
| spelling | Hida, Takeyuki Verfasser aut White Noise An Infinite Dimensional Calculus by Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit Dordrecht Springer Netherlands 1993 1 Online-Ressource (XIV, 520 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 253 Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in infinite dimensions based on white noise. By white noise we mean the generalized Gaussian process which is (informally) given by the time derivative of the Wiener process, i.e., by the velocity of Brownian mdtion. Therefore, in essence we present analysis on a Gaussian space, and applications to various areas of sClence. Calculus, analysis, and functional analysis in infinite dimensions (or dimension-free formulations of these parts of classical mathematics) have a long history. Early examples can be found in the works of Dirichlet, Euler, Hamilton, Lagrange, and Riemann on variational problems. At the beginning of this century, Frechet, Gateaux and Volterra made essential contributions to the calculus of functions over infinite dimensional spaces. The important and inspiring work of Wiener and Levy followed during the first half of this century. Moreover, the articles and books of Wiener and Levy had a view towards probability theory Mathematics Distribution (Probability theory) Quantum theory Computer engineering Probability Theory and Stochastic Processes Quantum Physics Electrical Engineering Mathematik Quantentheorie Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Weißes Rauschen (DE-588)4189502-2 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Weißes Rauschen (DE-588)4189502-2 s Funktionalanalysis (DE-588)4018916-8 s 1\p DE-604 Gauß-Prozess (DE-588)4156111-9 s 2\p DE-604 Kuo, Hui-Hsiung Sonstige oth Potthoff, Jürgen Sonstige oth Streit, Ludwig Sonstige oth https://doi.org/10.1007/978-94-017-3680-0 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 |
| spellingShingle | Hida, Takeyuki White Noise An Infinite Dimensional Calculus Mathematics Distribution (Probability theory) Quantum theory Computer engineering Probability Theory and Stochastic Processes Quantum Physics Electrical Engineering Mathematik Quantentheorie Funktionalanalysis (DE-588)4018916-8 gnd Weißes Rauschen (DE-588)4189502-2 gnd Gauß-Prozess (DE-588)4156111-9 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4189502-2 (DE-588)4156111-9 |
| title | White Noise An Infinite Dimensional Calculus |
| title_auth | White Noise An Infinite Dimensional Calculus |
| title_exact_search | White Noise An Infinite Dimensional Calculus |
| title_full | White Noise An Infinite Dimensional Calculus by Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit |
| title_fullStr | White Noise An Infinite Dimensional Calculus by Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit |
| title_full_unstemmed | White Noise An Infinite Dimensional Calculus by Takeyuki Hida, Hui-Hsiung Kuo, Jürgen Potthoff, Ludwig Streit |
| title_short | White Noise |
| title_sort | white noise an infinite dimensional calculus |
| title_sub | An Infinite Dimensional Calculus |
| topic | Mathematics Distribution (Probability theory) Quantum theory Computer engineering Probability Theory and Stochastic Processes Quantum Physics Electrical Engineering Mathematik Quantentheorie Funktionalanalysis (DE-588)4018916-8 gnd Weißes Rauschen (DE-588)4189502-2 gnd Gauß-Prozess (DE-588)4156111-9 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Quantum theory Computer engineering Probability Theory and Stochastic Processes Quantum Physics Electrical Engineering Mathematik Quantentheorie Funktionalanalysis Weißes Rauschen Gauß-Prozess |
| url | https://doi.org/10.1007/978-94-017-3680-0 |
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