H-1 BESSEL EXPANSIONS

Traditionally Bessel functions are considered in the spaces L(2)(0, 1; x) and L(2)(0, infinity; x), where the weight function x is the coeff icient of lambda in the formally self-adjoint differential equation -( xy')' + (n(2)/x)y = lambda xy, satisfied by the Bessel functions J(n)( root lambda x), J(-n)(root lambda x) and/or Y-n(root lambda x). We exa mine instead the same equation and its solutions in a Sobolev spaces H -1, generated in part by the left side of the differential equation. T he Bessel operators remain self-adjoint and their spectral resolutions remain the same in the new settings.