Modern Umbral Calculus : : An Elementary Introduction with Applications to Linear Interpolation and Operator Approximation Theory / / Francesco Aldo Costabile.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2019 Part 1
• VerfasserIn: Costabile, Francesco Aldo,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2019]; ©2019
• Year of Publication: 2019
• Language: English
• Series: De Gruyter Studies in Mathematics , 72
• Physical Description: 1 online resource (XVI)
• Other title: Frontmatter --; 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110652925; 9783110762464; 9783110719567; 9783110494938; 9783110616859; 9783110610765; 9783110664232; 9783110610406; 9783110606362
• ISSN: 0179-0986
• DOI: 10.1515/9783110652925
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Francesco Aldo Costabile.

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.