Extensions of Laguerre operators in indefinite inner product spaces.

The Laguerre-Sonin polynomials L are orthogonal in linear spaces with indefinite inner product if α<−1. We construct the completion Π( α) of this space and describe self-adjoint extensions of the Laguerre operator l(y)=xy″+(1+ α−x) y′, α<−1, in the space Π( α). In particular, we write out the self-adjoint extension of the Laguerre operator whose eigenfunctions coincide with the Laguerre-Sonin polynomials and form an orthogonal basis in Π( α). [ABSTRACT FROM AUTHOR]