Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Hardy spaces
Languages : en
Pages : 172

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Book Description

Author: J. P. Evans
Publisher:
ISBN:
Category : Functional analysis
Languages : en
Pages : 22

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Book Description
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.

Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 26

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Book Description

Author: O.B. Bekken
Publisher: Springer
ISBN: 3540382011
Category : Mathematics
Languages : en
Pages : 216

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Book Description

Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 64

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Book Description

Author: G. G. Lorentz
Publisher: American Mathematical Society
ISBN: 1470474948
Category : Mathematics
Languages : en
Pages : 200

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Book Description
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.

Author: John Garnett
Publisher: Springer Science & Business Media
ISBN: 0387497633
Category : Mathematics
Languages : en
Pages : 471

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Book Description
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.

Author:
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 336

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Book Description

Author: Thomas L. Miller
Publisher: American Mathematical Soc.
ISBN: 0821824155
Category : Mathematics
Languages : en
Pages : 137

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Book Description
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.

Author:
Publisher: Academic Press
ISBN: 0080874126
Category : Mathematics
Languages : en
Pages : 487

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Book Description
Bounded Analytic Functions