On the extension problem for accretive differential operators

Abstract

Let T 0 denote the minimal operator corresponding to the formal differential expression τy( x) = ( w( x)) −1 ∑ j = 0 n (−1) j ( p n − j ( x) y ( j) ) ( j) , x ϵ I, in L 2( I). Under the assumption that T 0 is an accretive operator in L 2( I) a complete description of all of the maximal accretive extensions of T 0 via explicit boundary conditions is given for a wide class of differential expressions τ.