Big-Planes, Boundaries and Function Algebras

Big-Planes, Boundaries and Function Algebras

1st Edition - March 2, 1992

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  • Author: T.V. Tonev
  • eBook ISBN: 9780080872834

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Treated in this volume are selected topics in analytic &Ggr;-almost-periodic functions and their representations as &Ggr;-analytic functions in the big-plane; n-tuple Shilov boundaries of function spaces, minimal norm principle for vector-valued functions and their applications in the study of vector-valued functions and n-tuple polynomial and rational hulls. Applications to the problem of existence of n-dimensional complex analytic structures, analytic &Ggr;-almost-periodic structures and structures of &Ggr;-analytic big-manifolds respectively in commutative Banach algebra spectra are also discussed.

Table of Contents

  • Chapter I: Uniform Algebras. Spectrum of an Algebra Element. Linear
    Multiplicative Functionals. Maximal Ideals. Some Examples. Shilov Boundary.
    Chapter II: &Ggr;-Analytic Functions in the Big-Plane. Generalized-analytic Functions. &Ggr;-analytic Functions on the Big-disc. The Big-disc Algebra. Boundary Behavior in the Big-disc. Algebras of
    &Ggr;v-analytic Functions. &Ggr;-entire Functions.
    Spectral Mappings of Semigroups. The Algebra
    HG. Algebras between
    HG and LG.
    Appendix. Analytic Measures. Chapter III: n-Tuple Shilov
    n-tuple Boundaries of Uniform Algebras.
    n-tuple Boundaries of Function Spaces. Properties of n-tuple Shilov Boundaries. Shilov Boundaries of Tensor Products. Multi-tuple
    Hulls. Chapter IV: Analytic Structures in Uniform Algebra Spectra.
    n-dimensional Manifolds in Spectra. Big-manifolds in Algebra
    Spectra. Almost Periodic and &Ggr;-analytic Structures. References. Index.

Product details

  • No. of pages: 293
  • Language: English
  • Copyright: © North Holland 1992
  • Published: March 2, 1992
  • Imprint: North Holland
  • eBook ISBN: 9780080872834

About the Author

T.V. Tonev

Affiliations and Expertise

Department of Mathematical Sciences, University of Montana, Missoula, MT, USA and Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria

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