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Big-Planes, Boundaries and Function Algebras

  • 1st Edition, Volume 172 - March 2, 1992
  • Latest edition
  • Author: T.V. Tonev
  • Language: English

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 Shilo… Read more

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Description

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. LinearMultiplicative 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 AlgebraHG∞. Algebras betweenHG∞ and LG∞.Appendix. Analytic Measures. Chapter III: n-Tuple ShilovBoundaries. n-tuple Boundaries of Uniform Algebras.n-tuple Boundaries of Function Spaces. Properties of n-tuple Shilov Boundaries. Shilov Boundaries of Tensor Products. Multi-tupleHulls. Chapter IV: Analytic Structures in Uniform Algebra Spectra.n-dimensional Manifolds in Spectra. Big-manifolds in AlgebraSpectra. Almost Periodic and &Ggr;-analytic Structures. References. Index.

Product details

  • Edition: 1
  • Latest edition
  • Volume: 172
  • Published: March 2, 1992
  • Language: English

About the author

TT

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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