Carroll, Robert W. On the canonical development of Parseval formulas for singular differential operators. (English) Zbl 0584.47052 Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 72, 65-70 (1982). As is well-known, Marčenko and Naimark a.o. have found a new framework for studying generalized Parseval formulas and eigenfunction expansions of differential operators since the early fifties. In this paper, applying certain aspects of Gasymov, the proof of a Parseval formula for singular differential operators modeled according to a radial Laplace-Beltrami operator is sketched. The details are contained in a recent monograph of the author. [Cf. R. Carroll, Transmutation, scattering theory and special functions (1982; Zbl 0494.34001)]. Reviewer: M.Mikolas Cited in 1 Document MSC: 47E05 General theory of ordinary differential operators 47A65 Structure theory of linear operators 34L99 Ordinary differential operators 47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces Keywords:generalized Parseval formulas; eigenfunction expansions of differential operators; singular differential operators; radial Laplace-Beltrami operator Citations:Zbl 0494.34001 PDFBibTeX XMLCite \textit{R. W. Carroll}, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 72, 65--70 (1982; Zbl 0584.47052)