However, it is important to note that the discrete-time model in the time scale formalism is given in terms of the difference operator
, and not in terms of the more conventional shift operator as, for example, in [1-3,13].
3) generalizes the divided difference operator
for G/B to what we call the highest root Hessenberg variety.
omega]] f(t) = f (t + [omega]) - f(t) / [omega] is the forward difference operator
with stepsize [omega] , and [D.
To establish the corresponding relation, let us first recall the definition of the backward difference operator
0]), and [DELTA] denotes the forward difference operator
, that is, [DELTA]x(n) = x(n +1) - x(n) for a sequence x(n).
for central difference, where L denotes the difference operator
generating the corresponding scheme and (*, *)O,h denotes the discrete [L.
where [delta] is the difference operator
, (Y/POP) is gross domestic product per capita, POP is total population, and [epsilon] and [micro] are zero-mean, serially uncorrelated random error terms.
The main concept of the time scale calculus is the so-called delta-derivative that is a generalization of both the time-derivative (in the continuous-time case) and the difference operator
(in the discrete-time case) .
1), we associate the linear difference operator
L defined by
Applying twice the basic difference operator
By linear algebra, one can prove that a certain multiple of the difference operator
In this section, we give a theorem which provides some estimates on these type of the inequality (2) about the forward difference operator