Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy

Advances in Difference Equations

Chao Wang²  Ravi P Agarwal⁴ 

[1] Department of Mathematics, Texas A&Department of Mathematics, Yunnan University, Kunming, People’M University-Kingsville, Kingsville, USA;s Republic of China

关键词: changing-periodic time scales;    decomposition theorem of time scales;    periodic sub-timescale;    almost periodic functions;    almost automorphic functions;    26E70;    43A60;    26E99;    34N05;    35B15;   

DOI  :  10.1186/s13662-015-0633-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this work, we address the periodic coverage phenomenon on arbitrary unbounded time scales and initiate a new idea, namely, we introduce the concept of changing-periodic time scales. We discuss some properties of this new concept and illustrate several examples. Specially, we establish a basic decomposition theorem of time scales which provides bridges between periodic time scales and an arbitrary time scale with a bounded graininess function μ. Based on this result, we introduce local-almost periodic and local-almost automorphic functions on changing-periodic time scales and study some related properties. The concept of changing-periodic time scales introduced in this paper will help in understanding and removing the serious deficiency which arises in the study of classical functions on time scales.

【 授权许可】

CC BY