Chebyshev Splines and Kolmogorov Inequalities

Sergey Bagdasarov

ISBN 10: 3764359846 / ISBN 13: 9783764359843

Published by Berlin Springer Springer, 1998

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular, an extensive account is given of structural, limiting, and extremal properties of perfect w-splines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev w-splines and w-polynomials associated with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geometrical methods are developed based on entirely new ideas. The book can be used profitably by pure or applied scientists looking for mathematical approaches to the solution of practical problems for which standard methods do not work. The scope of problems treated in the monograph, ranging from the maximization of integral functionals, characterization of the structure of equimeasurable functions, construction of Chebyshev splines through applications of fixed point theorems to the solution of integral equations related to the classical Euler equation, appeals to mathematicians specializing in approximation theory, functional and convex analysis, optimization, topology, and integral equations. 210 pp. Englisch.

Seller Inventory # 9783764359843

Bibliographic Details

• Title: Chebyshev Splines and Kolmogorov Inequalities
• Publisher: Berlin Springer Springer
• Publication Date: 1998
• Language: English
• ISBN 10: 3764359846
• ISBN 13: 9783764359843
• Binding: Buch
• Condition: Neu
• Dimensions: 240W x 170H x 18D millimeters 240 millimeters width by 170 millimeters height by 18 millimeters depth
• Weight: 565 grams

About this title

Synopsis

This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular, an extensive account is given of structural, limiting, and extremal properties of perfect w-splines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev w-splines and w-polynomials associated with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geometrical methods are developed based on entirely new ideas. The book can be used profitably by pure or applied scientists looking for mathematical approaches to the solution of practical problems for which standard methods do not work. The scope of problems treated in the monograph, ranging from the maximization of integral functionals, characterization of the structure of equimeasurable functions, construction of Chebyshev splines through applications of fixed point theorems to the solution of integral equations related to the classical Euler equation, appeals to mathematicians specializing in approximation theory, functional and convex analysis, optimization, topology, and integral equations

.