Fock spaces connected with spherical mean operator and associated operators
Following ideas of \textit{V.\,Bargmann} [Commun.\ Pure Appl.\ Math.\ 14, 187--214 (1961; Zbl 0107.09102); Proc.\ Natl.\ Acad.\ Sci.\ USA 48, 199--204 (1962; Zbl 0107.09103)] and \textit{F.\,M.\thinspace Cholewinsky} [SIAM J.~Math.\ Anal.\ 15, 177--202 (1984; Zbl 0596.46017)], the authors define the Fock space \(F\) associated with the spherical mean operator to be the space of entire functions on \(\mathbb C\times\mathbb C^n\), which are even in the first variable and square integrable with respect to a certain measure expressed through the Mac Donald function \(K_{(n-1)/2}(\cdot)\). Some results for the Segal-Bargmann transform and for Toeplitz operators in this space are established.
scientific article; zbMATH DE number 5578113