Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1994
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| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
8 |
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| Online-Zugang: | Volltext |
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| 100 | 1 | |a Khenkin, G. M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Several Complex Variables II |b Function Theory in Classical Domains Complex Potential Theory |c edited by G. M. Khenkin, A. G. Vitushkin |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1994 | |
| 300 | |a 1 Online-Ressource (VII, 262 p) | ||
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| 490 | 0 | |a Encyclopaedia of Mathematical Sciences |v 8 |x 0938-0396 | |
| 500 | |a Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given | ||
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-57882-3 |
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| id | DE-604.BV042422689 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:23:26Z |
| institution | BVB |
| isbn | 9783642578823 9783642633911 |
| issn | 0938-0396 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858106 |
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| physical | 1 Online-Ressource (VII, 262 p) |
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| publishDate | 1994 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Encyclopaedia of Mathematical Sciences |
| spelling | Khenkin, G. M. Verfasser aut Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory edited by G. M. Khenkin, A. G. Vitushkin Berlin, Heidelberg Springer Berlin Heidelberg 1994 1 Online-Ressource (VII, 262 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 8 0938-0396 Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given Mathematics Geometry, algebraic Potential theory (Mathematics) Algebraic topology Algebraic Geometry Algebraic Topology Potential Theory Theoretical, Mathematical and Computational Physics Mathematik Vitushkin, A. G. Sonstige oth https://doi.org/10.1007/978-3-642-57882-3 Verlag Volltext |
| spellingShingle | Khenkin, G. M. Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory Mathematics Geometry, algebraic Potential theory (Mathematics) Algebraic topology Algebraic Geometry Algebraic Topology Potential Theory Theoretical, Mathematical and Computational Physics Mathematik |
| title | Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory |
| title_auth | Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory |
| title_exact_search | Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory |
| title_full | Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory edited by G. M. Khenkin, A. G. Vitushkin |
| title_fullStr | Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory edited by G. M. Khenkin, A. G. Vitushkin |
| title_full_unstemmed | Several Complex Variables II Function Theory in Classical Domains Complex Potential Theory edited by G. M. Khenkin, A. G. Vitushkin |
| title_short | Several Complex Variables II |
| title_sort | several complex variables ii function theory in classical domains complex potential theory |
| title_sub | Function Theory in Classical Domains Complex Potential Theory |
| topic | Mathematics Geometry, algebraic Potential theory (Mathematics) Algebraic topology Algebraic Geometry Algebraic Topology Potential Theory Theoretical, Mathematical and Computational Physics Mathematik |
| topic_facet | Mathematics Geometry, algebraic Potential theory (Mathematics) Algebraic topology Algebraic Geometry Algebraic Topology Potential Theory Theoretical, Mathematical and Computational Physics Mathematik |
| url | https://doi.org/10.1007/978-3-642-57882-3 |
| work_keys_str_mv | AT khenkingm severalcomplexvariablesiifunctiontheoryinclassicaldomainscomplexpotentialtheory AT vitushkinag severalcomplexvariablesiifunctiontheoryinclassicaldomainscomplexpotentialtheory |