Moduli Of Smoothness

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Moduli Of Smoothness

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Author : Z. Ditzian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Moduli Of Smoothness written by Z. Ditzian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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 . . . . . . .

The Averaged Moduli Of Smoothness

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Author : Blagovest Sendov
language : en
Publisher:
Release Date : 1988

The Averaged Moduli Of Smoothness written by Blagovest Sendov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

The authors outline this new theory of estimating the error in commonly used numerical methods, including interpolation, approximation of function by means of operators and quadrature formulae. The advantage of this theory is that it allows the error to be estimated for an approximation method.

Moduli Of Smoothness

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Author : Z. Ditzian
language : en
Publisher:
Release Date : 1987-10-01

Moduli Of Smoothness written by Z. Ditzian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-10-01 with categories.

Complex Analysis And Potential Theory

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Author : Tahir Aliyev Azero?lu
language : en
Publisher: World Scientific
Release Date : 2007

Complex Analysis And Potential Theory written by Tahir Aliyev Azero?lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This volume gathers the contributions from outstanding mathematicians, such as Samuel Krushkal, Reiner Kuhnau, Chung Chun Yang, Vladimir Miklyukov and others.It will help researchers to solve problems on complex analysis and potential theory and discuss various applications in engineering. The contributions also update the reader on recent developments in the field. Moreover, a special part of the volume is completely devoted to the formulation of some important open problems and interesting conjectures.

The Geometry Of Moduli Spaces Of Sheaves

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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-27

The Geometry Of Moduli Spaces Of Sheaves written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-27 with Mathematics categories.

This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Approximation Theory And Harmonic Analysis On Spheres And Balls

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Author : Feng Dai
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Approximation Theory And Harmonic Analysis On Spheres And Balls written by Feng Dai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Methods Of Fourier Analysis And Approximation Theory

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Author : Michael Ruzhansky
language : en
Publisher: Birkhäuser
Release Date : 2016-03-11

Methods Of Fourier Analysis And Approximation Theory written by Michael Ruzhansky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-11 with Mathematics categories.

Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

Hardy Littlewood And Ulyanov Inequalities

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Author : Yurii Kolomoitsev
language : en
Publisher: American Mathematical Society
Release Date : 2021-09-24

Hardy Littlewood And Ulyanov Inequalities written by Yurii Kolomoitsev and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-24 with Mathematics categories.

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Theory And Applications Of Differentiable Functions Of Several Variables

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Author : Sergei Mikhailovich Nikol'skii
language : en
Publisher: American Mathematical Soc.
Release Date : 1967

Theory And Applications Of Differentiable Functions Of Several Variables written by Sergei Mikhailovich Nikol'skii and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Differentiable functions categories.

Proceedings Of The Second Asian Mathematical Conference 1995

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Author : S Tangmanee
language : en
Publisher: World Scientific
Release Date : 1998-02-17

Proceedings Of The Second Asian Mathematical Conference 1995 written by S Tangmanee and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-17 with categories.

This proceedings volume covers the main fields of mathematics: analysis, algebra and number theory, geometry and topology, combinatorics and graphs, applied mathematics, numerical analysis and computer mathematics, probability and statistics, teaching and popularization of mathematics.