Abstract
Abstract The paper determines a non-classical Bittner operational calculus model, in which the derivative is understood as an -symmetric difference Dm,n {x (k)} := {x (k+m)− x (k− n). By considering an operation Dm,n,b {x (k)} := {x (k+m)− b (k)x (k− n), the formulated model has been generalized.
Highlights
), called the derivative, is a surjection
It easy to verify that the limit conditions are projections of onto the subspace
If we define the objects (1), we have in mind a representation, or a model of the operational calculus
Summary
We have from the definition (9) of the integrals , we get the following. Each sequence that is a constant for the derivative (8) is a - periodic sequence. From the definition (10) of limit conditions there follows the below Corollary 2. The numbers form a cycle of the - periodic sequence
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