Integral Operators in the Theory of Linear Partial Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1961
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
23 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information |
| Beschreibung: | 1 Online-Ressource (X, 148 p) |
| ISBN: | 9783642649851 9783642649875 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-64985-1 |
Internformat
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Datensatz im Suchindex
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| author | Bergman, Stefan |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-64985-1 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642649851 9783642649875 |
| issn | 0071-1136 |
| language | English |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Bergman, Stefan Verfasser aut Integral Operators in the Theory of Linear Partial Differential Equations by Stefan Bergman Berlin, Heidelberg Springer Berlin Heidelberg 1961 1 Online-Ressource (X, 148 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 23 0071-1136 The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information Mathematics Mathematics, general Mathematik Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Integraloperator (DE-588)4131247-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Integraloperator (DE-588)4131247-8 s 1\p DE-604 Lineare partielle Differentialgleichung (DE-588)4167708-0 s 2\p DE-604 https://doi.org/10.1007/978-3-642-64985-1 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 | Bergman, Stefan Integral Operators in the Theory of Linear Partial Differential Equations Mathematics Mathematics, general Mathematik Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Integraloperator (DE-588)4131247-8 gnd |
| subject_GND | (DE-588)4167708-0 (DE-588)4044779-0 (DE-588)4131247-8 |
| title | Integral Operators in the Theory of Linear Partial Differential Equations |
| title_auth | Integral Operators in the Theory of Linear Partial Differential Equations |
| title_exact_search | Integral Operators in the Theory of Linear Partial Differential Equations |
| title_full | Integral Operators in the Theory of Linear Partial Differential Equations by Stefan Bergman |
| title_fullStr | Integral Operators in the Theory of Linear Partial Differential Equations by Stefan Bergman |
| title_full_unstemmed | Integral Operators in the Theory of Linear Partial Differential Equations by Stefan Bergman |
| title_short | Integral Operators in the Theory of Linear Partial Differential Equations |
| title_sort | integral operators in the theory of linear partial differential equations |
| topic | Mathematics Mathematics, general Mathematik Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Integraloperator (DE-588)4131247-8 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Lineare partielle Differentialgleichung Partielle Differentialgleichung Integraloperator |
| url | https://doi.org/10.1007/978-3-642-64985-1 |
| work_keys_str_mv | AT bergmanstefan integraloperatorsinthetheoryoflinearpartialdifferentialequations |