The perturbation theory of linear operators concerns itself with the eigenvalues and eigenelements of a variable operator. If T(e) is an operator depending on a real parameter e, the relation between the eigenvalues and eigenelements of the perturbed operator T(e) (e?^0) and those of the unperturbed operator 7\0) is of particular interest. This theory finds considerable application in the field...

This paper deals with spectral type differential equations of the self-adjoint differential operator, 2r order: L(2r)[Y ](x)= 1 (x) d dxr ( (x) r (x) dY (x) dxr ) = rnY (x). If (x) is the weight function and (x) is a second degree polynomial function, then the corresponding classical orthogonal polynomials, {Qn(x)}∞n=0, are shown to satisfy this differential equation when rn is given by rn = r−...