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Uniform algebras and Jensen measures /
These lecture notes are devoted to an area of current research interest that bridges functional analysis and function theory. The unifying theme is the notion of subharmonicity with respect to a uniform algebra. The topics covered include the rudiments of Choquet theory, various classes of represent...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1978.
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| Colección: | London Mathematical Society lecture note series ;
32. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Preface; 1. Choquettheory; R-measures; The R-measures are called Jensen measures.; The Family S of R-envelope Functions; The Family S of Continuous R-envelope Functions; The R-Dirichlet Problem; The Choquet Boundary; Barriers; Maximal Measures; Examples; References; 2 . Classes of representing measures; Representing Measures; Arens-Singer Measures; An Example; Nomenclature; References; 3 . The algebra R(K); References; 4 . The corona problem for Riemann surfaces; References; 5 . Subharmonicity with respect to a uniformalgebra; Quasi-subharmonic Functions
- Hartogs SeriesLocalization Principle for Subharmonic Functions; Localization of the Jensen Boundary; Supports of Jensen Measures; Bremermann Functions; Evidently E is a compact subset of U; The Generalized Dirichlet Problem; References; 6 . Algebras of analytic functions; Plurisubharmonic Functions; Plurisubharmonic Barriers and Pseudoconvex Boundary Points; Bremermann's Theorem; Bremermann Functions; Br erne rmann f un c t i on.; Bremermann's Generalized Dirichlet Problem; References; 7 . The conjugation operation for representingmeasures; The Conjugation Operator; Cole's Theorem