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On the canonical development of Parseval formulas for singular differential operators. (English) Zbl 0584.47052

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

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

Citations:

Zbl 0494.34001
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