On the difference quotient operator.

摘要

If G is a bounded, open, connected subset of the complex plane, containing the origin, we define H;The primary goal of this thesis is the characterization of the difference quotient operator in terms of the more familiar multiplication operator and the description of some of its properties.;The difference quotient operator T: H;Theorem 1. T is unitarily equivalent to some compact perturbation of the adjoint of the multiplication operator M;Theorem 2. T has commutative commutant.;The third result concerns the multiplication operator M;Theorem 3. M;A different section of this thesis is concerned with Bishop's operator. We prove.;Theorem 4. Let T