On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators

Abstract

The second-order symmetric Sturm-Liouville differential expressions τ 1 , τ 2 , … , τ n with real coefficients are considered on the interval I = ( a , b ) , − ∞ ≤ a b ≤ ∞ . It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).