Difference Equations in Spaces of Regular Functions: A Tribute To Salvatore Pincherle
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Pincherle studies the surjectivity of a difference operator with constant coefficients in the space of holomorphic functions. In this paper, we discuss how this work can be rephrased in the context of modern functional analysis and we conclude by extending his results and we show that difference equations act surjectively on the space of quaternionic regular functions.
Salvatore Pincherle, surjectivity, difference operators, holomorphic functions, functional analysis, quaternions
Algebra | Analysis | History of Science, Technology, and Medicine | Ordinary Differential Equations and Applied Dynamics
Sabidini, I., & Struppa, D.C. (2012). Difference equations in spaces of regular functions: A tribute to Salvatore Pincherle. In S. Coen (Ed.), Mathematicians in Bologna 1861–1960 (pp. 427-438). doi: 10.1007/978-3-0348-0227-7__18
In S. Coen (Ed.), Mathematicians in Bologna 1861–1960. Dr. Struppa's chapter begins on page 427.