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Modern Umbral Calculus: An Elementary Introduction with Applications to Linear Interpolation and Operator Approximation Theory

โœ Scribed by Francesco Aldo Costabile

Publisher
De Gruyter
Year
2019
Tongue
English
Leaves
276
Series
De Gruyter Studies in Mathematics; 72
Category
Library
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โœฆ Synopsis

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

โœฆ Table of Contents

Preface
Acknowledgment
Contents
Acronyms
Part I: Introduction
1. Preliminaries and notations
2. Particular matrices and their connections with formal power series
Part II: Polynomial sequences of binomial type
3. Binomial polynomial sequences
4. Applications to linear interpolation and operators approximation theory
5. Examples
Part III: Appell polynomial sequences
6. Appell polynomial sequences
7. Application to linear interpolation and approximation theory
8. Examples
Part IV: Sheffer polynomial sequences
9. Sheffer polynomial sequence
10. Applications to linear interpolation and operators approximation theory
11. Examples
Part V: Lidstone polynomial sequences
12. Lidstone-type polynomial sequences
13. Application to linear interpolation and operators approximation theory
14. Examples
Bibliography
Index

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