
346
M. Bertero and C. De Mol
A
It has been shown [3] that s commutes with the following differential operator
(D.~f)($)
- -[(t 2 - 1)("/2- t2)ft(t)] ! + 2(t 2 -
1)f(t) . (16)
The appropriate self-adjoint extension of this operator is obtained by requiring that the
functions in the domain of D.~ are bounded at the boundary points t = 1 and t = 3' (notice
A
that the differential equation
(D~f)(z) = # f(z)
has five regular singular points in the
complex plane, one being the point at infinity). In the limit 7 ~ 1, the operator (16)
reduces, after a change of variable, to the ...