Diamond-alpha Polynomial Series on Time Scales
Classical Analysis and ODEs
2008-09-10 v1
Abstract
The objective of this paper is twofold: (i) to survey existing results of generalized polynomials on time scales, covering definitions and properties for both delta and nabla derivatives; (ii) to extend previous results by using the more general notion of diamond-alpha derivative on time scales. We introduce a new notion of combined-polynomial series on a time scale, as a convex linear combination of delta and nabla generalized series. Main results are formulated for homogenous time scales. As an example, we compute diamond-alpha derivatives on time scales for delta and nabla exponential functions.
Keywords
Cite
@article{arxiv.0805.0274,
title = {Diamond-alpha Polynomial Series on Time Scales},
author = {Dorota Mozyrska and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:0805.0274},
year = {2008}
}
Comments
Accepted to the 8th Portuguese Conference on Automatic Control -- CONTROLO'2008, 21 to 23 July 2008, UTAD University, Vila Real, Portugal