Abstract
Abstract
In this paper, we introduce the concept of almost-complete-closed time scales (ACCTS) that allows independent variables of functions to possess almost-periodicity under translations. For this new type of time scale, a class of piecewise functions with double-almost-periodicity is proposed and studied. Based on these, concepts of weighted pseudo-double-almost-periodic functions (WPDAP) in Banach spaces and a translation-almost-closed set are introduced. Further, we prove that the function space WPDAP0 affiliated to WPDAP is a translation-almost-closed set. Then, by introducing the concept of almost-uniform convergence for piecewise functions on ACCTS and using measure theory on time scales, some composition theorems of WPDAP and the completeness of the function space are proved.
Funder
Youth Fund of NSFC
Tian Yuan Fund of NSFC
Dong Lu Youth Excellent Teachers Development Program of Yunnan University
IRTSTYN and Joint Key Project of Yunnan Provincial Science and Technology Department of Yunnan University
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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