Berezanskij, Yu. M.; Kalyuzhnij, A. A. Hypercomplex systems with locally compact bases. (English. Russian original) Zbl 0632.43003 Sel. Math. Sov. 4, 151-200 (1985); translation from Prepr., Inst. Mat. Akad. Nauk. Ukr. SSR, Kiev 82.40 (1982). In this paper the authors give an extensive and detailed exposition of the theory of hypercomplex systems with locally compact bases Q and construct basic elements of harmonic analysis on them. They make use of a “structural measure” \(\gamma\) (A,B,r), where A, B are subsets of Q and \(r\in Q\), which plays the role of the “cubical matrix” in the classical case of a finite set Q. These results continue the theory developed by the first author in several previous papers. There is a wide bibliography containing several recent contributions on this subject. Reviewer: C.Vinti Cited in 1 Document MSC: 43A05 Measures on groups and semigroups, etc. 43A99 Abstract harmonic analysis Keywords:hypergroups; hypercomplex systems; locally compact bases; structural measure; bibliography PDFBibTeX XMLCite \textit{Yu. M. Berezanskij} and \textit{A. A. Kalyuzhnij}, Sel. Math. Sov. 4, 151--200 (1985; Zbl 0632.43003); translation from Prepr., Inst. Mat. Akad. Nauk. Ukr. SSR, Kiev 82.40 (1982)