ABSTRACT
The operators that are of most significance in the theory to follow are D, E, , ∆. These operators are defined for functions u(x) of a complex variable x by
(1.1)
The operator D is, of course, the derivative operator; E is the translation operator; is
the forward difference quotient operator; and ∆, which corresponds to for ω=1, is the
forward difference operator. Other operators of interest are defined by
(1.2)
and known as the backward difference quotient, the central difference quotient, and the central mean, respectively. The corresponding operators for ω=1 are designated by , δ, µ, respectively.
