New Almost Periodic Type Functions and Solutions of Differential Equations
- 1 December 1996
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 48 (6) , 1138-1153
- https://doi.org/10.4153/cjm-1996-059-9
Abstract
Let X be a Banach space and . Let Π and Π0 be two subspaces of , the Banach space of bounded continuous functions from 𝕁 to X. We seek conditions under which Π + Π0 is closed in . This led to introduce a general space, which contains many classes of almost periodic type functions as subspaces. We prove some recent results on indefinite integral for the elements of these classes. We apply certain results on harmonic analysis to investigate solutions of differential equations. As an application we study specific spaces: the spaces of asymptotic and pseudo almost automorphic functions and their solutions of some ordinary quasi-linear and a non-linear parabolic partial differential equations.Keywords
This publication has 11 references indexed in Scilit:
- Polynomials and functions with finite spectra on locally compact Abelian groupsBulletin of the Australian Mathematical Society, 1995
- Pseudo Almost Periodic Solutions of Some Differential EquationsJournal of Mathematical Analysis and Applications, 1994
- Ergodic theorems for semigroups of operatorsProceedings of the American Mathematical Society, 1992
- Éléments ergodiques et totalement ergodiques dans $L^{∞}(Γ)$Studia Mathematica, 1981
- Almost automorphic functions and totally bounded groupsRocky Mountain Journal of Mathematics, 1977
- Almost-Periodic Functions and Functional EquationsPublished by Springer Nature ,1971
- Rhythmische Abbildungen abelscher Gruppen IIProbability Theory and Related Fields, 1967
- Almost Automorphic Functions on GroupsAmerican Journal of Mathematics, 1965
- A NEW APPROACH TO ALMOST PERIODICITYProceedings of the National Academy of Sciences, 1962
- Abstract ergodic theorems and weak almost periodic functionsTransactions of the American Mathematical Society, 1949