Weighted Composition Operators on the Mittag-Leffler Spaces of Entire Functions

摘要

The subject of this manuscript is the investigation of (possibly unbounded) weighted composition operators arising from the formal expression E(psi, phi) f = psi center dot f circle phi over Mittag-Leffler spaces of entire functions. In this context, the functions. and. are entire functions, and this manuscript presents basic operator theoretic properties such as closability, invertibility, cyclicity, complex symmetry, boundedness, compactness, and the essential norm. Significantly, a characterization of. and. are obtained for bounded weighted composition operators over the Mittag-Leffler space of entire functions for parameter 0 < alpha < 2, and many extant results in the Fock space are reproduced in the more general context of Mittag-Leffler spaces.