Uniform Algebras and Jensen Measures

These lecture notes are devoted to an area of current research interest that bridges functional analysis and function theory.

T. W. Gamelin (Author)

9780521222808, Cambridge University Press

Paperback, published 1 March 1979

172 pages
22.8 x 15.2 x 1 cm, 0.27 kg

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.

1. Choquet Theory
2. Classes of Representing Measures
3. The Algebra R(K)
4. The Corona Problem for Riemann Surfaces
5. Subharmonicity with Respect to a Uniform Algebra
6. Algebras of Analytic Functions
7. The Conjugation Operation for Representing Measures
8. The Conjugation Operation for Jensen Measures
9. Moduli of Functions in H2(o).

Subject Areas: Algebra [PBF]