Topics in Uniform Approximation of Continuous Functions PDF Download
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Author: Ileana Bucur
Publisher: Springer Nature
ISBN: 3030484122
Category : Mathematics
Languages : en
Pages : 140
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Book Description
This book presents the evolution of uniform approximations of continuous functions. Starting from the simple case of a real continuous function defined on a closed real interval, i.e., the Weierstrass approximation theorems, it proceeds up to the abstract case of approximation theorems in a locally convex lattice of (M) type. The most important generalizations of Weierstrass’ theorems obtained by Korovkin, Bohman, Stone, Bishop, and Von Neumann are also included. In turn, the book presents the approximation of continuous functions defined on a locally compact space (the functions from a weighted space) and that of continuous differentiable functions defined on ¡n. In closing, it highlights selected approximation theorems in locally convex lattices of (M) type. The book is intended for advanced and graduate students of mathematics, and can also serve as a resource for researchers in the field of the theory of functions.
Author: Ileana Bucur
Publisher: Springer Nature
ISBN: 3030484122
Category : Mathematics
Languages : en
Pages : 140
Get Book
Book Description
This book presents the evolution of uniform approximations of continuous functions. Starting from the simple case of a real continuous function defined on a closed real interval, i.e., the Weierstrass approximation theorems, it proceeds up to the abstract case of approximation theorems in a locally convex lattice of (M) type. The most important generalizations of Weierstrass’ theorems obtained by Korovkin, Bohman, Stone, Bishop, and Von Neumann are also included. In turn, the book presents the approximation of continuous functions defined on a locally compact space (the functions from a weighted space) and that of continuous differentiable functions defined on ¡n. In closing, it highlights selected approximation theorems in locally convex lattices of (M) type. The book is intended for advanced and graduate students of mathematics, and can also serve as a resource for researchers in the field of the theory of functions.
Author: Vladislav K. Dzyadyk
Publisher: Walter de Gruyter
ISBN: 3110208245
Category : Mathematics
Languages : en
Pages : 497
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Book Description
A thorough, self-contained and easily accessible treatment of the theory on the polynomial best approximation of functions with respect to maximum norms. The topics include Chebychev theory, Weierstraß theorems, smoothness of functions, and continuation of functions.
Author: Theodore J. Rivlin
Publisher: Courier Corporation
ISBN: 9780486640693
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Mathematics of Computing -- Numerical Analysis.
Author: J.G. Llavona
Publisher: Elsevier
ISBN: 9780080872414
Category : Mathematics
Languages : en
Pages : 240
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Book Description
This self-contained book brings together the important results of a rapidly growing area. As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells' theorem and Aron's theorem for the fine topology of order m; extension of Bernstein's and Weierstrass' theorems for infinite dimensional Banach spaces; extension of Nachbin's and Whitney's theorem for infinite dimensional Banach spaces; automatic continuity of homomorphisms in algebras of continuously differentiable functions, etc.
Author: Ronald A. De Vore
Publisher: Springer
ISBN: 3540379959
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Author: Theodore J. Rivlin
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 168
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Book Description
Approximation theory is an area of mathematics with important practical applications in computation. This volume provides an introduction to the theoretical foundations which underlie many of the algorithms of everyday use. For each method of approximation studied, at least one algorithm leading to actual numerical approximations is described.
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: Ronald A. De Vore
Publisher:
ISBN: 9783662179765
Category :
Languages : en
Pages : 304
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Book Description
Author: Isidor Pavlovich Natanson
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 252
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Book Description
Author:
Publisher: Elsevier
ISBN: 9780080871363
Category : Mathematics
Languages : en
Pages : 218
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Book Description
This work deals with the many variations of the Stoneileierstrass Theorem for vector-valued functions and some of its applications. The book is largely self-contained. The amount of Functional Analysis required is minimal, except for Chapter 8. The book can be used by graduate students who have taken the usual first-year real and complex analysis courses.
