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Modern Umbral Calculus
An Elementary Introduction with Applications to Linear Interpolation and Operator Approximation Theory
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Francesco Aldo Costabile
Language:
English
Published/Copyright:
2019
About this book
This book presents a novel approach to umbral calculus, which uses only elementary linear algebra (matrix calculus) based on the observation that there is an isomorphism between Sheffer polynomials and Riordan matrices, and that Sheffer polynomials can be expressed in terms of determinants. Additionally, applications to linear interpolation and operator approximation theory are presented in many settings related to various families of polynomials.
- Presents a novel approach to umbral calculus based on linear algebra
- Covers connections with interpolation and approximation theory
- Of interest to graduate students and researchers in analysis and numerical mathematics
Author / Editor information
Francesco Aldo Costabile, University of Calabria, Italy.
Topics
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Frontmatter
I -
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Preface
VII -
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Acknowledgment
IX -
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Contents
XI -
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Acronyms
XV - Part I: Introduction
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1. Preliminaries and notations
3 -
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2. Particular matrices and their connections with formal power series
7 - Part II: Polynomial sequences of binomial type
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3. Binomial polynomial sequences
23 -
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4. Applications to linear interpolation and operators approximation theory
41 -
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5. Examples
47 - Part III: Appell polynomial sequences
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6. Appell polynomial sequences
77 -
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7. Application to linear interpolation and approximation theory
101 -
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8. Examples
107 - Part IV: Sheffer polynomial sequences
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9. Sheffer polynomial sequence
149 -
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10. Applications to linear interpolation and operators approximation theory
167 -
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11. Examples
175 - Part V: Lidstone polynomial sequences
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12. Lidstone-type polynomial sequences
203 -
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13. Application to linear interpolation and operators approximation theory
217 -
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14. Examples
223 -
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Bibliography
245 -
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Index
255
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 17, 2019
eBook ISBN:
9783110652925
Hardcover published on:
June 17, 2019
Hardcover ISBN:
9783110649963
Pages and Images/Illustrations in book
Front matter:
16
Coloured Illustrations:
30
Tables:
15
Audience(s) for this book
Graduate students and researchers in mathematics and computer science.
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
