Invariant potential theory in the unit ball of Cn̳ /:
This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's functio...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1994.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
199. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables. |
| Beschreibung: | On t.p. "n̳" is superscript. |
| Beschreibung: | 1 online resource (x, 173 pages) |
| Bibliographie: | Includes bibliographical references (pages 164-169) and index. |
| ISBN: | 9781107362109 1107362105 |
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| 520 | |a This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables. | ||
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| contents | Cover; Half-title; Title; Copyright; Dedication; Contents; Introduction; 1. Notation and Preliminary Results; 1.1 Notation; 1.2 Integral Formulas on B; 1.3 Automorphisms of B; 2. The Bergman Kernel; 2.1 The Bergman Kernel; 2.2 Examples; 2.3 Properties of the Bergman Kernel; 2.4 The Bergman Metric; 3. The Laplace-Beltrami Operator; 3.1 The Invariant Laplacian; 3.2 The Invariant Laplacian for Un; 3.3 The Invariant Laplacian for B; 3.4 The Invariant Gradient; 4. Invariant Harmonic and Subharmonic Functions; 4.1 M.-Subharmonic Functions; 4.2 The Invariant Convolution on B; 4.3 The Riesz Measure 10.3 M-Harmonic Bergman and Dirichlet Spaces10.4 Remarks; References; Index |
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| indexdate | 2024-10-25T16:21:21Z |
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| spelling | Stoll, Manfred. Invariant potential theory in the unit ball of Cn̳ / Manfred Stoll. Cambridge ; New York : Cambridge University Press, 1994. 1 online resource (x, 173 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 199 On t.p. "n̳" is superscript. Includes bibliographical references (pages 164-169) and index. Print version record. This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables. Cover; Half-title; Title; Copyright; Dedication; Contents; Introduction; 1. Notation and Preliminary Results; 1.1 Notation; 1.2 Integral Formulas on B; 1.3 Automorphisms of B; 2. The Bergman Kernel; 2.1 The Bergman Kernel; 2.2 Examples; 2.3 Properties of the Bergman Kernel; 2.4 The Bergman Metric; 3. The Laplace-Beltrami Operator; 3.1 The Invariant Laplacian; 3.2 The Invariant Laplacian for Un; 3.3 The Invariant Laplacian for B; 3.4 The Invariant Gradient; 4. Invariant Harmonic and Subharmonic Functions; 4.1 M.-Subharmonic Functions; 4.2 The Invariant Convolution on B; 4.3 The Riesz Measure 10.3 M-Harmonic Bergman and Dirichlet Spaces10.4 Remarks; References; Index Potential theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85105671 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Unit ball. http://id.loc.gov/authorities/subjects/sh85139717 Théorie du potentiel. Invariants. Boule unité. MATHEMATICS Complex Analysis. bisacsh Invariants fast Potential theory (Mathematics) fast Unit ball fast Potentiaaltheorie. gtt Teoria do potencial. larpcal Análise matemática. larpcal Potentiel, théorie du. ram Invariants. ram Print version: Stoll, Manfred. Invariant potential theory in the unit ball of Cn̳. Cambridge ; New York : Cambridge University Press, 1994 0521468302 (DLC) 94220904 (OCoLC)31607057 London Mathematical Society lecture note series ; 199. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552468 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552468 Volltext |
| spellingShingle | Stoll, Manfred Invariant potential theory in the unit ball of Cn̳ / London Mathematical Society lecture note series ; Cover; Half-title; Title; Copyright; Dedication; Contents; Introduction; 1. Notation and Preliminary Results; 1.1 Notation; 1.2 Integral Formulas on B; 1.3 Automorphisms of B; 2. The Bergman Kernel; 2.1 The Bergman Kernel; 2.2 Examples; 2.3 Properties of the Bergman Kernel; 2.4 The Bergman Metric; 3. The Laplace-Beltrami Operator; 3.1 The Invariant Laplacian; 3.2 The Invariant Laplacian for Un; 3.3 The Invariant Laplacian for B; 3.4 The Invariant Gradient; 4. Invariant Harmonic and Subharmonic Functions; 4.1 M.-Subharmonic Functions; 4.2 The Invariant Convolution on B; 4.3 The Riesz Measure 10.3 M-Harmonic Bergman and Dirichlet Spaces10.4 Remarks; References; Index Potential theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85105671 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Unit ball. http://id.loc.gov/authorities/subjects/sh85139717 Théorie du potentiel. Invariants. Boule unité. MATHEMATICS Complex Analysis. bisacsh Invariants fast Potential theory (Mathematics) fast Unit ball fast Potentiaaltheorie. gtt Teoria do potencial. larpcal Análise matemática. larpcal Potentiel, théorie du. ram Invariants. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85105671 http://id.loc.gov/authorities/subjects/sh85067665 http://id.loc.gov/authorities/subjects/sh85139717 |
| title | Invariant potential theory in the unit ball of Cn̳ / |
| title_auth | Invariant potential theory in the unit ball of Cn̳ / |
| title_exact_search | Invariant potential theory in the unit ball of Cn̳ / |
| title_full | Invariant potential theory in the unit ball of Cn̳ / Manfred Stoll. |
| title_fullStr | Invariant potential theory in the unit ball of Cn̳ / Manfred Stoll. |
| title_full_unstemmed | Invariant potential theory in the unit ball of Cn̳ / Manfred Stoll. |
| title_short | Invariant potential theory in the unit ball of Cn̳ / |
| title_sort | invariant potential theory in the unit ball of cn |
| topic | Potential theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85105671 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Unit ball. http://id.loc.gov/authorities/subjects/sh85139717 Théorie du potentiel. Invariants. Boule unité. MATHEMATICS Complex Analysis. bisacsh Invariants fast Potential theory (Mathematics) fast Unit ball fast Potentiaaltheorie. gtt Teoria do potencial. larpcal Análise matemática. larpcal Potentiel, théorie du. ram Invariants. ram |
| topic_facet | Potential theory (Mathematics) Invariants. Unit ball. Théorie du potentiel. Boule unité. MATHEMATICS Complex Analysis. Invariants Unit ball Potentiaaltheorie. Teoria do potencial. Análise matemática. Potentiel, théorie du. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552468 |
| work_keys_str_mv | AT stollmanfred invariantpotentialtheoryintheunitballofcn |