Abstract

A General Left-Definite Theory with Applications to Differential Equations L. Littlejohn (joint work with Richard Wellman) In this talk, we present a general left-definite theory for self-adjoint operators A that are bounded below in a Hilbert space H. We show that, in this case, there exists a continuum of unique left-definite Hilbert spaces and a continuum of unique left-definite self-adjoint operators associated with (H,A). As an example, we discuss the applications of these results to the classical second-order Laguerre differential equation.

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