The L problem of moments in two dimensions

AbstractThe classical solution to the L problem of moments due to N. I. Akhiezer and M. G. Krein is partially generalized to the two-dimensional case. A parallel between the apparently quite different one-dimensional and two-dimensional L problems of moments is established by means of the theories of the phase shift and of the principal function. This point of view brings into the field the geometry of Hilbert spaces and the analysis of the pairs of not necessarily commuting self-adjoint operators acting on them