THE LAGUERRE TYPE OPERATOR IN A LEFT DEFINITE HILBERT-SPACE

This article completes earlier work concerning the Laguerre type diffe rential operator of fourth order, set in a weighted Sobolev space on [ 0, infinity). It is shown that the operator, which is self-adjoint in L(2)(0, infinity; e(-x)) (X) R, is also self-adjoint in the new space, whose inner product also involves first and second derivatives. Furth er, the spectrum remains unchanged, the Laguerre type polynomials are eigenfunctions, and the spectral resolution, associated with the opera tor, is still an eigenfunction expansion. (C) 1995 Academic Press, Inc .