Boehmians on manifolds (Q5926124)

Boehmians were first constructed as generalizations of regular Mikusiński operators [cf. \textit{J. Mikusiński} and \textit{P. Mikusiński}, C. R. Acad. Sci., Paris, Ser. 1, 293, 463-464 (1981; Zbl 0495.44006)]. Almost all papers on Boehmians published to date concern objects defined on \(\mathbb{R}^N\). The construction of Boehmians on a manifold requires a commutative convolution structure. In this paper such construtions for multidimensional tori and spheres are presented. Then conditions under which the construction of Boehmians on a manifold is possible are given.