Potential Theory: An Analytic and Probabilistic Approach to Balayage
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | During the last thirty years potential theory has undergone a rapid development, much of which can still only be found in the original papers. This book deals with one part of this development, and has two aims. The first is to give a comprehensive account of the close connection between analytic and probabilistic potential theory with the notion of a balayage space appearing as a natural link. The second aim is to demonstrate the fundamental importance of this concept by using it to give a straight presentation of balayage theory which in turn is then applied to the Dirichlet problem. We have considered it to be beyond the scope of this book to treat further topics such as duality, ideal boundary and integral representation, energy and Dirichlet forms. The subject matter of this book originates in the relation between classical potential theory and the theory of Brownian motion. Both theories are linked with the Laplace operator. However, the deep connection between these two theories was first revealed in the papers of S. KAKUTANI [1], [2], [3], M. KAC [1] and J. L. DO DB [2] during the period 1944-54: This can be expressed by the fact that the harmonic measures which occur in the solution of the Dirichlet problem are hitting distributions for Brownian motion or, equivalently, that the positive hyperharmonic functions for the Laplace equation are the excessive functions of the Brownian semigroup |
| Beschreibung: | 1 Online-Ressource (XIII, 435p) |
| ISBN: | 9783642711312 9783540163961 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-71131-2 |
Internformat
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.96 |
| dewey-search | 515.96 |
| dewey-sort | 3515.96 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-71131-2 |
| format | Electronic eBook |
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| id | DE-604.BV042422956 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642711312 9783540163961 |
| issn | 0172-5939 |
| language | English |
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| physical | 1 Online-Ressource (XIII, 435p) |
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| spelling | Bliedtner, Jürgen Verfasser aut Potential Theory An Analytic and Probabilistic Approach to Balayage by Jürgen Bliedtner, Wolfhard Hansen Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (XIII, 435p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 During the last thirty years potential theory has undergone a rapid development, much of which can still only be found in the original papers. This book deals with one part of this development, and has two aims. The first is to give a comprehensive account of the close connection between analytic and probabilistic potential theory with the notion of a balayage space appearing as a natural link. The second aim is to demonstrate the fundamental importance of this concept by using it to give a straight presentation of balayage theory which in turn is then applied to the Dirichlet problem. We have considered it to be beyond the scope of this book to treat further topics such as duality, ideal boundary and integral representation, energy and Dirichlet forms. The subject matter of this book originates in the relation between classical potential theory and the theory of Brownian motion. Both theories are linked with the Laplace operator. However, the deep connection between these two theories was first revealed in the papers of S. KAKUTANI [1], [2], [3], M. KAC [1] and J. L. DO DB [2] during the period 1944-54: This can be expressed by the fact that the harmonic measures which occur in the solution of the Dirichlet problem are hitting distributions for Brownian motion or, equivalently, that the positive hyperharmonic functions for the Laplace equation are the excessive functions of the Brownian semigroup Mathematics Potential theory (Mathematics) Potential Theory Mathematik Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s 1\p DE-604 Hansen, Wolfhard Sonstige oth https://doi.org/10.1007/978-3-642-71131-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bliedtner, Jürgen Potential Theory An Analytic and Probabilistic Approach to Balayage Mathematics Potential theory (Mathematics) Potential Theory Mathematik Potenzialtheorie (DE-588)4046939-6 gnd |
| subject_GND | (DE-588)4046939-6 |
| title | Potential Theory An Analytic and Probabilistic Approach to Balayage |
| title_auth | Potential Theory An Analytic and Probabilistic Approach to Balayage |
| title_exact_search | Potential Theory An Analytic and Probabilistic Approach to Balayage |
| title_full | Potential Theory An Analytic and Probabilistic Approach to Balayage by Jürgen Bliedtner, Wolfhard Hansen |
| title_fullStr | Potential Theory An Analytic and Probabilistic Approach to Balayage by Jürgen Bliedtner, Wolfhard Hansen |
| title_full_unstemmed | Potential Theory An Analytic and Probabilistic Approach to Balayage by Jürgen Bliedtner, Wolfhard Hansen |
| title_short | Potential Theory |
| title_sort | potential theory an analytic and probabilistic approach to balayage |
| title_sub | An Analytic and Probabilistic Approach to Balayage |
| topic | Mathematics Potential theory (Mathematics) Potential Theory Mathematik Potenzialtheorie (DE-588)4046939-6 gnd |
| topic_facet | Mathematics Potential theory (Mathematics) Potential Theory Mathematik Potenzialtheorie |
| url | https://doi.org/10.1007/978-3-642-71131-2 |
| work_keys_str_mv | AT bliedtnerjurgen potentialtheoryananalyticandprobabilisticapproachtobalayage AT hansenwolfhard potentialtheoryananalyticandprobabilisticapproachtobalayage |