UID:
almafu_9959239091302883
Umfang:
1 online resource (162 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88377-1
,
1-107-36581-3
,
1-107-37054-X
,
1-107-36090-0
,
1-107-36969-X
,
1-299-40362-X
,
1-107-36335-7
,
0-511-66240-8
Serie:
London Mathematical Society lecture note series ; 32
Inhalt:
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 representing measures, the duality between abstract sub-harmonic functions and Jensen measures, applications to problems of approximation of plurisubharmonic functions of several complex variables, and Cole's theory of estimates for conjugate functions. Many of the results are published here for the first time in monograph form.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
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
,
The M-Riesz EstimateEstimates of Zygmund; The Kolmogoroff Estimate; Notes on Sources; References; 8 . The conjugation operation for Jensenmeasures; The M.Riesz Estimate for Jensen Measures; Cole's Theorem; Sharp Constants; Arens-Singer Measures; Notes on Sources; References; 9 . Moduli of functions in H2 (σ); References; List of notation; Index
,
English
Weitere Ausg.:
ISBN 0-521-22280-X
Sprache:
Englisch
Fachgebiete:
Mathematik
URL:
https://doi.org/10.1017/CBO9780511662409
Bookmarklink
