Approximation by Bounded Analytic Functions to Functions Represented by Dirichlet Series
Approximation by Bounded Analytic Functions to Functions Represented by Dirichlet Series

Author: J. P. Evans

Publisher:

Published: 1961

Total Pages: 22

ISBN-13:

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Results concerning approximation to functions analytic on a closed point set R̄0 by arbitrary functions analytic and bounded in a region R1 containing R̄0 were first established by Walsh [4] in 1938 and later extended by the present writers to the limiting case where R̄0 and the boundary of R1 have points in common [5]. It is the purpose of the present note to continue the study of this problem now in situations where the approximated function is no longer assumed analytic at points common to the boundaries of R0 and R1.

Bounded Analytic Functions
Bounded Analytic Functions

Author: John Garnett

Publisher: Springer Science & Business Media

Published: 2007-04-05

Total Pages: 471

ISBN-13: 0387497633

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This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available.

Approximation of Functions
Approximation of Functions

Author: G. G. Lorentz

Publisher: American Mathematical Society

Published: 2023-05-08

Total Pages: 200

ISBN-13: 1470474948

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This is an easily accessible account of the approximation of functions. It is simple and without unnecessary details, but complete enough to include the classical results of the theory. With only a few exceptions, only functions of one real variable are considered. A major theme is the degree of uniform approximation by linear sets of functions. This encompasses approximations by trigonometric polynomials, algebraic polynomials, rational functions, and polynomial operators. The chapter on approximation by operators does not assume extensive knowledge of functional analysis. Two chapters cover the important topics of widths and entropy. The last chapter covers the solution by Kolmogorov and Arnol?d of Hilbert's 13th problem. There are notes at the end of each chapter that give information about important topics not treated in the main text. Each chapter also has a short set of challenging problems, which serve as illustrations.

Subnormal Operators and Representations of Algebras of Bounded Analytic Functions and Other Uniform Algebras
Subnormal Operators and Representations of Algebras of Bounded Analytic Functions and Other Uniform Algebras

Author: Thomas L. Miller

Publisher: American Mathematical Soc.

Published: 1986

Total Pages: 137

ISBN-13: 0821824155

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The present memoir lies between operator theory and function theory of one complex variable. Motivated by refinements of the analytic functional calculus of a subnormal operator, the authors are rapidly directed towards difficult problems of hard analysis. Quite specifically, the basic objects to be investigated in this paper are the unital (continuous) algebra homomorphisms [lowercase Greek]Pi : [italic]H[exponent infinity symbol]([italic]G) [rightwards arrow] [italic]L([italic]H), with the additional property that [lowercase Greek]Pi([italic]z) is a subnormal operator.