Two integral operators in Clifford analysis
Monogenic functions are generalizations of holomorphic functions in one complex variable to \(\mathbb{R}^{n+1}\) variable. Let \(M_2(\mathbb{R}^{n+1})\) be the monogenic Fock space obtained by the completion of the space of monogenic polynomials and \(\mathcal{F}_2(\mathbb{C}^n)\) be the Fock space of holomorphic functions in \(\mathbb{C}^n\) (Segal-Bargmann space). The objective of this paper is to study the connections between \(\mathcal{F}_2(\mathbb{C}^n)\) and \(M_2(\mathbb{R}^{n+1})\). Two integral operators are defined connecting these two spaces with the help of exponential functions in Clifford analysis.
scientific article; zbMATH DE number 5555200
scientific article