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 ...
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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 . . . . . . .
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Add this copy of Moduli of Smoothness to cart. $21.86, very good condition, Sold by Hay-on-Wye Booksellers rated 4.0 out of 5 stars, ships from Hereford, UNITED KINGDOM, published 1987 by Springer.
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Very Good. Spine of cover has slightly faded and some minor shelf wear. Also inscriptions on fep but content is fine.. Sewn binding. Cloth over boards. 225 p. Graduate Texts in Mathematics, 9.
Add this copy of Moduli of Smoothness to cart. $25.86, good condition, Sold by Hay-on-Wye Booksellers rated 4.0 out of 5 stars, ships from Hereford, UNITED KINGDOM, published 1987 by Springer.
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Good. Minor scratch on front cover, minor shelfwear to bookcovers and its extremities, without dustjacket, previous owners signature on the inside front cover and title page, otherwise fine. Sewn binding. Cloth over boards. 225 p. Graduate Texts in Mathematics, 9.
Add this copy of Moduli of Smoothness (Springer Series in Computational to cart. $61.54, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1987 by Springer Verlag.
