Holomorphe Störungstheorie in lokalkonvexen Räumen.
The purpose of this paper is to study the Sarason’s problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols and , we establish a necessary and sufficient condition for the boundedness of some Toeplitz products subjected to certain restriction on and . We also characterize this property in terms of the Berezin transform.
Outline. In this paper I discuss some quantitative aspects related to power bounded operators T and to the decay of . For background I refer to two recent surveys J. Zemánek [1994], C. J. K. Batty [1994]. Here I try to complement these two surveys in two different directions. First, if the decay of is as fast as O(1/n) then quite strong conclusions can be made. The situation can be thought of as a discrete version of analytic semigroups; I try to motivate this in Section 1 by demonstrating the...