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.
Author(s): T. W. Gamelin
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 1978
Language: English
Pages: 171
Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
1. Choquet Theory......Page 10
2. Classes of Representing Measures......Page 31
3. The Algebra R(K)......Page 43
4. The Corona Problem for Riemann Surfaces......Page 55
5. Subharmonicity with Respect to a Uniform Algebra......Page 63
6. Algebras of Analytic Functions......Page 92
7. The Conjugation Operation for Representing Measures......Page 116
8. The Conjugation Operation for Jensen Measures......Page 138
9. Moduli of Functions in H 2 (o)......Page 155
List of Notation......Page 165
Index......Page 167
