Spectral synthesis of diagonal operators and representing systems for the space of entire functions |
| |
Authors: | Steven M. Seubert J. Gordon Wade |
| |
Affiliation: | Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221, USA |
| |
Abstract: | In this paper, we study continuous linear operators on spaces of functions analytic on disks in the complex plane having as eigenvectors the monomials zn whose associated eigenvalues λn are distinct. In particular, we show that under mild conditions, such a diagonal operator has non-spectral invariant subspaces (that is, closed invariant subspaces which are not the closed linear span of collections of monomials) if and only if every entire function of a particular growth rate is representable as a generalized Dirichlet series . |
| |
Keywords: | Diagonal operators Spectral synthesis Entire functions Dirichlet series |
本文献已被 ScienceDirect 等数据库收录! |