C*-Algebras of Singular Integral operators on the line realted to singular Sturm-Liouville problems.
We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.
We prove an existence theorem for connected branches of solutions to nonlinear operator equations in Banach spaces. This abstract result is applied to the asymptotically equivalent solutions to nonlinear ordinary differential equations.