An abstract scheme of the method of limit operators and some of its applications. (Q1432594)

Limit operators appeared for the first time in the paper of \textit{J. Favard} [Acta Math. 51, 31--81 (1927; JFM 53.0409.02)] where the existence of almost periodic solutions to ordinary differential equations with almost periodic coefficients was studied. \textit{Eh. N. Mukhamadiev} [Sov. Math. Dokl. 13, 1122--1126 (1972); translation from Dokl. Akad. Nauk SSSR 205, 1292--1295 (1972; Zbl 0273.47024) and Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 110, 120--140 (1981; Zbl 0508.47046)] applied limit operators to the problem of the solvability of elliptic partial differential equations. Then the method was applied by the present author for studying the Fredholm property for some classes of pseudodifferential and convolution operators. In the paper under review, an abstract scheme of this method is suggested. This scheme may be applied to the cases mentioned above. Here, this scheme is applied to the new problem of Fredholmness for convolution operators on some groups.