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100%: Ditzian, Z. and Vilmos Totik: Moduli of Smoothness. (ISBN: 9783540965367) 1987, in Deutsch, Broschiert.Nur diese Ausgabe anzeigen…
100%: Z. Ditzian, Vilmos Totik: Moduli of Smoothness (ISBN: 9781461291510) 1984, in Englisch, Taschenbuch.Nur diese Ausgabe anzeigen…
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Moduli of Smoothness (1984)
~EN PB NWISBN: 9781461291510 bzw. 1461291518, vermutlich in Englisch, Springer Shop, Taschenbuch, neu.
Lieferung aus: Deutschland, Lagernd.
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 . . . . . . . Soft cover.
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 . . . . . . . Soft cover.
2
Moduli of Smoothness (1984)
~EN NWISBN: 9781461291510 bzw. 1461291518, vermutlich in Englisch, neu.
Lieferung aus: Kanada, Lagernd, zzgl. Versandkosten.
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 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 . . . . . . .
3
Moduli of Smoothness
EN NWISBN: 9781461291510 bzw. 1461291518, in Englisch, Springer-Verlag New York Inc. neu.
Lieferung aus: Vereinigtes Königreich Großbritannien und Nordirland, in-stock.
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 Smoothn.
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 Smoothn.
4
Moduli of Smoothness. (1987)
DE HC USISBN: 9783540965367 bzw. 354096536X, in Deutsch, Springer-Verlag GmbH, gebundenes Buch, gebraucht.
Von Händler/Antiquariat, Antiquariat Braun [822365], Gengenbach, Germany.
227 Seiten. Gebundene Ausgabe. *Ausgeschiedene Bibliotheksdublette, Vorsatz bzw. Titel mehrfach gestempelt. Rücken mit Bibliotheksaufkleber. Ansonsten sauber und gut erhalten. - Ex library copy. Several stamps on title and endpaper, library label on spine. Inside in good condition. ISBN 9783540965367 Sprache: Englisch Gewicht in Gramm: 800.
227 Seiten. Gebundene Ausgabe. *Ausgeschiedene Bibliotheksdublette, Vorsatz bzw. Titel mehrfach gestempelt. Rücken mit Bibliotheksaufkleber. Ansonsten sauber und gut erhalten. - Ex library copy. Several stamps on title and endpaper, library label on spine. Inside in good condition. ISBN 9783540965367 Sprache: Englisch Gewicht in Gramm: 800.
5
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Moduli of Smoothness. (1987)
DEISBN: 9783540965367 bzw. 354096536X, in Deutsch, Springer, Berlin/Heidelberg, Deutschland.
Lieferung aus: Deutschland, Versandkosten in die BRD.
Von Händler/Antiquariat, Antiquariat Bernd Braun.
Springer-Verlag, GmbH, 227 Seiten. Gebundene Ausgabe. *Ausgeschiedene Bibliotheksdublette, Vorsatz bzw. Titel mehrfach gestempelt. Rücken mit Bibliotheksaufkleber. Ansonsten sauber und gut erhalten. - Ex library copy. Several stamps on title and endpaper, library label on spine. Inside in good condition. ISBN 9783540965367Natwiss - Mathematik 1987.
Von Händler/Antiquariat, Antiquariat Bernd Braun.
Springer-Verlag, GmbH, 227 Seiten. Gebundene Ausgabe. *Ausgeschiedene Bibliotheksdublette, Vorsatz bzw. Titel mehrfach gestempelt. Rücken mit Bibliotheksaufkleber. Ansonsten sauber und gut erhalten. - Ex library copy. Several stamps on title and endpaper, library label on spine. Inside in good condition. ISBN 9783540965367Natwiss - Mathematik 1987.
6
Moduli of Smoothness
EN NWISBN: 9781461291510 bzw. 1461291518, in Englisch, Springer New York, neu.
Lieferung aus: Kanada, In Stock, plus shipping.
Z. Ditzian, Vilmos Totik, Books, Science and Nature, Moduli of Smoothness, The book introduces a new way of measuring smoothness. The need for this new concept arises from the failure of the classical moduli of smoothness to solve some basic problems, such as characterizing the behaviour of best polynomial approximation in Lp -1,1 . The new modulus, which has a simple form, can also be described as a Peetre K functional between an Lp space and a weighted Sobolev space. Connections between interpolation of spaces and approximation theory are utilized in applying the modulus of smoothness. The applications include best (weighted) polynomial approximation on a finite interval, characterization of the rate of approximation given by classical operator processes such as Bernstein, Kantorovich, Szasz-Mirakjan, and Post-Widder operators, Freud-type weighted polynomial approximation on infinite intervals with exponentially decreasing weights and polynomial approximation in several variables. Special emphasis is placed on the computability aspect of the moduli. The results are new, and complete proofs are given. It is hoped that the book will be of interest and useful for mathematicians working in approximation theory, interpolation of spaces, numerical analysis and real analysis.
Z. Ditzian, Vilmos Totik, Books, Science and Nature, Moduli of Smoothness, The book introduces a new way of measuring smoothness. The need for this new concept arises from the failure of the classical moduli of smoothness to solve some basic problems, such as characterizing the behaviour of best polynomial approximation in Lp -1,1 . The new modulus, which has a simple form, can also be described as a Peetre K functional between an Lp space and a weighted Sobolev space. Connections between interpolation of spaces and approximation theory are utilized in applying the modulus of smoothness. The applications include best (weighted) polynomial approximation on a finite interval, characterization of the rate of approximation given by classical operator processes such as Bernstein, Kantorovich, Szasz-Mirakjan, and Post-Widder operators, Freud-type weighted polynomial approximation on infinite intervals with exponentially decreasing weights and polynomial approximation in several variables. Special emphasis is placed on the computability aspect of the moduli. The results are new, and complete proofs are given. It is hoped that the book will be of interest and useful for mathematicians working in approximation theory, interpolation of spaces, numerical analysis and real analysis.
7
Moduli of Smoothness. (1987)
DE HCISBN: 9783540965367 bzw. 354096536X, in Deutsch, Springer, Berlin/Heidelberg, Deutschland, gebundenes Buch.
Von Händler/Antiquariat, Kloof Booksellers & Scientia Verlag [18355], Amsterdam, Netherlands.
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
8
Moduli of Smoothness (1987)
DE HC USISBN: 9783540965367 bzw. 354096536X, in Deutsch, 227 Seiten, Springer Berlin, gebundenes Buch, gebraucht.
Lieferung aus: Deutschland, Versandfertig in 1 - 2 Werktagen.
Von Händler/Antiquariat, Wissenschaftliches Buch.
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
Von Händler/Antiquariat, Wissenschaftliches Buch.
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
10
Moduli of Smoothness
EN NWISBN: 9781461291510 bzw. 1461291518, in Englisch, Springer Science+Business Media, neu.
Lieferung aus: Vereinigte Staaten von Amerika, In Stock.
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
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