Symmetric multiparameter problems and deficiency index theory

Abstract

In this article we study the multiparameter generalization of standard deficiency index theory. A classical result in this area states that if T is a symmetric operator in a Hilbert space then the dimension of the null space of T*−λI, λ∈ℂ, is constant for λ belonging to the upper (or lower) half-plane and further, when these two constants are equal, T admits a self-adjoint extension.