Francesco Aldo Costabile 
Modern Umbral Calculus [PDF ebook] 
An Elementary Introduction with Applications to Linear Interpolation and Operator Approximation Theory

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.

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