Yurii Stefanovych Samoilenko, an outstanding Ukrainian mathematician, was bom on September 17. 1943, in Vladimirovka village, Volgograd region, Russia. His father, Stefan Pylypovych Samiylenko, was a widely known Ukrainian philologist. In 1965. Yu. S. Samoilenko graduated from Dnipropetrovsk State University, where he studied Mathematics and obtained, in particular, good background in Function theory, which remains a traditional research domain in that university. Since 1967, his life is closely related with Institute of Mathematics, Ukrainian National Academy of Sciences. In 1967 he became a Ph.D. student of Yu. M. Berezansky, who introduced the young scientist into Kyiv Functional Analysis school. First papers by Yu. S. Samoilenko are devoted to integral representations of positive-definite matrix kernel, invariant with respect to certain transformation groups, and they formed a basis of his Ph.D. thesis, prepared under a supervision of Yu. M. Berezansky, which was completed to a Ph.D. degree in 1970. A progress in developing mathematical models of physics stimulated further interest to infinite-dimensional analysis, especially to the spectral theory of infinite families of self-adjoint operators, which became one of the main research areas of Yu. M. Berezansky's research group. Yu. S. Samoilenko obtained a series of results in this area. One of the most cited ones is a construction and study of a nuclear space A of analytic functions of an infinite number of variables (with Yu. G. Kondratiev, 1978). A natural ouestion that arose was a possibility to obtain similar spectral decompositions for non-commuting families of operators, in particular, families satisfying certain kinds of algebraic relations.

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