On Laguerre Operator Associated With Extension And Spectral Analysis

In this paper, we study self-adjoint extensions and their spectrum of Laguerrc operator defined on the domain I = (0,8). We give all self-adjoint extensions of L and study a family of special extensions, i.e., Weyl-Titchmarsh extensions, in particular. We discuss the Friedrichs extension of L. We obtain that the spectral set of any self-adjoint extension is discrete and find a self-adjoint extension T0 of L which satisfies moreover, we point out that this is the unique one possessing such a property; for any self-adjoint extension T of L different from T0, the spectra of T are zeros of a function corresponding to it.