Adjoints of elliptic cone operators

Abstract

We study the adjointness problem for the closed extensions of a general b-elliptic operator A in x^{-ν}Diff^m_b(M;E), ν>0, initially defined as an unbounded operator A:C_c^\infty(M;E)\subset x^μL^2_b(M;E)\to x^μL^2_b(M;E), μ\in \R. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.