Differences of vector-valued functions on topological groups
Open Access
- 1 July 1996
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 124 (7) , 1969-1975
- https://doi.org/10.1090/s0002-9939-96-03258-3
Abstract
Let G G be a locally compact group equipped with right Haar measure. The right differences △ h φ \triangle _{h} \varphi of functions φ \varphi on G G are defined by △ h φ ( t ) = φ ( t h ) − φ ( t ) \triangle _{h}\varphi (t) = \varphi (th) - \varphi (t) for h , t ∈ G h,t \in G . Let φ ∈ L ∞ ( G ) \varphi \in L^{\infty }(G) and suppose △ h φ ∈ L p ( G ) \triangle _{h} \varphi \in L^{p} (G) for some 1 ≤ p > ∞ 1 \leq p > \infty and all h ∈ G h \in G . We prove that ‖ △ h φ ‖ p \Vert \triangle _{h} \varphi \Vert _{p} is a right uniformly continuous function of h h . If <math...This publication has 6 references indexed in Scilit:
- Polynomials and functions with finite spectra on locally compact Abelian groupsBulletin of the Australian Mathematical Society, 1995
- Differences of functions in locally convex spaces and applications to almost periodic and almost automorphic functionsAnnales Polonici Mathematici, 1983
- Joint Continuity of Separately Continuous FunctionsProceedings of the American Mathematical Society, 1981
- Abstract Harmonic AnalysisPublished by Springer Nature ,1979
- Separate continuity and joint continuityPacific Journal of Mathematics, 1974
- Functional AnalysisPublished by Springer Nature ,1974