Spectrum of Operator Induced by Holomorphic Vector Field
by
E. Pourreza
University of Tabriz, Iran
Coauthors: A.I. Shahbazov

Poster

Let D subset Cⁿ(n >= 1) be a bounded domain and A(D) the space of all functions which are holomorphic on D and continous on [`D]. We will consider the operator induced by some holomorphic vector field defined on some neighbourhood of [`D] (may be is non-transversal at some points of \partialD ), of the form

f --> ó õ \infty 0  u(\phi(t, x))f(\phi(t, x))d\mu(t)

acting on A(D) - Banach modules which are subspaces of HOL(D) where u in A(D) is a fixed function, \phi is the integral curve of the vector field and \mu is a finite complex regular Borel measure on R₊=[0, +\infty).

In this article we will construct for this operator" admissible " approximation when it is compact, and will investigate spectrum of these " admissible" operators, which are very important in solving and existence of solutions of integro- diffrential equations which are define by dynamical systems.

Date received: May 18, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadq-48.