Potential Theory on Locally Compact Abelian Groups:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1975
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
87 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-642-66128-0 |
| Beschreibung: | Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brownian motion is determined by its semigroup of transition probabilities, the Brownian semigroup, and the connection between classical potential theory and the theory of Brownian motion can be described analytically in the following way: The Laplace operator is the infinitesimal generator for the Brownian semigroup and the Newtonian potential kernel is the" integral" of the Brownian semigroup with respect to time. This connection between classical potential theory and the theory of Brownian motion led Hunt (cf. Hunt [2]) to consider general "potential theories" defined in terms of certain stochastic processes or equivalently in terms of certain semi groups of operators on spaces of functions. The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group. (ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a potential, respectively a harmonic function; this property of classical potential theory can also be expressed by saying that the Laplace operator is a differential operator with constant co efficients |
| Umfang: | 1 Online-Ressource (VIII, 200 p) |
| ISBN: | 9783642661280 9783642661303 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-66128-0 |
Internformat
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| 490 | 0 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 87 |x 0071-1136 | |
| 500 | |a Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brownian motion is determined by its semigroup of transition probabilities, the Brownian semigroup, and the connection between classical potential theory and the theory of Brownian motion can be described analytically in the following way: The Laplace operator is the infinitesimal generator for the Brownian semigroup and the Newtonian potential kernel is the" integral" of the Brownian semigroup with respect to time. This connection between classical potential theory and the theory of Brownian motion led Hunt (cf. Hunt [2]) to consider general "potential theories" defined in terms of certain stochastic processes or equivalently in terms of certain semi groups of operators on spaces of functions. The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group. (ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a potential, respectively a harmonic function; this property of classical potential theory can also be expressed by saying that the Laplace operator is a differential operator with constant co efficients | ||
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Datensatz im Suchindex
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| author_variant | c b cb |
| building | Verbundindex |
| bvnumber | BV042422899 |
| classification_tum | MAT 000 |
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| dewey-sort | 3510 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-66128-0 |
| format | Electronic eBook |
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| id | DE-604.BV042422899 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:47Z |
| institution | BVB |
| isbn | 9783642661280 9783642661303 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858316 |
| oclc_num | 863788728 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VIII, 200 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spellingShingle | Berg, Christian Potential Theory on Locally Compact Abelian Groups Mathematics Mathematics, general Mathematik Lokal kompakte Gruppe (DE-588)4168094-7 gnd Potenzialtheorie (DE-588)4046939-6 gnd Lokal kompakte Abelsche Gruppe (DE-588)4168093-5 gnd Abelsche Gruppe (DE-588)4140988-7 gnd |
| subject_GND | (DE-588)4168094-7 (DE-588)4046939-6 (DE-588)4168093-5 (DE-588)4140988-7 |
| title | Potential Theory on Locally Compact Abelian Groups |
| title_auth | Potential Theory on Locally Compact Abelian Groups |
| title_exact_search | Potential Theory on Locally Compact Abelian Groups |
| title_full | Potential Theory on Locally Compact Abelian Groups by Christian Berg, Gunnar Forst |
| title_fullStr | Potential Theory on Locally Compact Abelian Groups by Christian Berg, Gunnar Forst |
| title_full_unstemmed | Potential Theory on Locally Compact Abelian Groups by Christian Berg, Gunnar Forst |
| title_short | Potential Theory on Locally Compact Abelian Groups |
| title_sort | potential theory on locally compact abelian groups |
| topic | Mathematics Mathematics, general Mathematik Lokal kompakte Gruppe (DE-588)4168094-7 gnd Potenzialtheorie (DE-588)4046939-6 gnd Lokal kompakte Abelsche Gruppe (DE-588)4168093-5 gnd Abelsche Gruppe (DE-588)4140988-7 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Lokal kompakte Gruppe Potenzialtheorie Lokal kompakte Abelsche Gruppe Abelsche Gruppe |
| url | https://doi.org/10.1007/978-3-642-66128-0 |
| work_keys_str_mv | AT bergchristian potentialtheoryonlocallycompactabeliangroups AT forstgunnar potentialtheoryonlocallycompactabeliangroups |