Moduli of Smoothness

Language: English

Published by Springer, Springer Okt 2011, 2011

1461291518 / 9781461291510

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This item is printed on demand - Print on Demand Titel. Neuware -The subject of this book is the introduction and application of a new measure for smoothness offunctions. Though we have both previously published some articles in this direction, the results given here are new. Much of the work was done in the summer of 1984 in Edmonton when we consolidated earlier ideas and worked out most of the details of the text. It took another year and a half to improve and polish many of the theorems. We express our gratitude to Paul Nevai and Richard Varga for their encouragement. We thank NSERC of Canada for its valuable support. We also thank Christine Fischer and Laura Heiland for their careful typing of our manuscript. z. Ditzian V. Totik CONTENTS Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 PART I. THE MODULUS OF SMOOTHNESS Chapter 1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1. Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2. Discussion of Some Conditions on cp(x). . . . ¿ . . . . . . . ¿ . . ¿ . . ¿ ¿ . 8 . . . ¿ . 1.3. Examples of Various Step-Weight Functions cp(x) . . ¿ . . ¿ . . ¿ . . ¿ . . . 9 . . ¿ Chapter 2. The K-Functional and the Modulus of Continuity . . . 10 2.1. The Equivalence Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . 2.2. The Upper Estimate, Kr.tp(f, tr)p ~ Mw;(f, t)p, Case I . . . . . . . . . . . . 12 . . . 2.3. The Upper Estimate of the K-Functional, The Other Cases. . . . . . . . . . 16 . 2.4. The Lower Estimate for the K-Functional. . . . . . . . . . . . . . . . . . . 20 . . . . . Chapter 3. K-Functionals and Moduli of Smoothness, Other Forms. 24 3.1. A Modified K-Functional. . . . . . . . . . . . . . . . . . . . . . . . . . 24 . . . . . . . . . . 3.2. Forward and Backward Differences. . . . . . . . . . . . . . . . . . . . . . 26 . . . . . . . 3.3. Main-Part Modulus of Smoothness. . . . . . . . . . . . . . . . . . . . . . 28 . . . . . . .Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 240 pp. Englisch.

Seller Inventory # 9781461291510

Title
Moduli of Smoothness
Author
Z. Ditzian
Publisher
Springer, Springer Okt 2011
Publication year
2011
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
1461291518
ISBN 13
9781461291510
Item weight
371 grams
Dimensions
235x155x14 mm

buchversandmimpf2000

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