Spectral exp nsion of self-conjoint operators on generalized elements of a Hilbert space
The author discusses spectral expansions of generalized eigen-elements belonging to systems derived in the article (Ukrainian Mathematical Journal, vol. 12, N 1, 1960). The necessary and sufficient condition of the possibility of such expansions was obtained. Some generalizations are discussed, as well as a supplement to the estimate of the growth of eigen-functions and the interpretation of «eigen-subspaces» of self-adjoint operators.
Citation Example: Kats G. I. Spectral exp nsion of self-conjoint operators on generalized elements of a Hilbert space // Ukr. Mat. Zh. - 1961. - 13, № 4. - pp. 13-33.