Abstract
xeR3 acting on functions in P( 1x1< 1) vanishing on 1x1 = 1. We set x = 1x1 and assume q(x) is a real-valued function in L*( [0, 11). The closure H of I? is a self-adjoint operator with compact resolvent. Hence H has pure point spectrum without finite accumulation points. Moreover, using the mapping U(X) + xu(x) and expansion in spherical harmonics, one shows that H is unitarily equivalent to a direct sum of Sturm-Liouville operators acting on L*[O, 11, cf. [ 11. The first operator in this sum is
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