On the limit-classifications of even and odd-order formally symmetric differential expressions

Abstract

In this paper we consider the formally symmetric differential expression M[·] of any order (odd or even) ≥ 2. We characterise the dimension of the quotient spaceis the sesquilinear form in f and g associated with M. These results generalise the wellknown theorem that M is in the limit-point case at ∞ if and only if [ f g](∞) = 0 for every f , g ∈ the maximal domain ∆ associated with M.Keywords. Limit classification, minimal and maximal closed operators; symmetric operators, self-adjoint operators; quotient space D(T max )/D(T min ).