Spectral estimates for resolvent differences of self-adjoint elliptic operators (Q395610)

In view of applications to the analysis of elliptic boundary value problems, the first two authors of the paper under review had proposed in [J. Funct. Anal. 243, No.~2, 536--565 (2007; Zbl 1132.47038)] a generalization of the classical concept of boundary triple associated to the adjoint of a symmetric operator \(A\) acting in a Hilbert space \({\mathcal{H}}\), namely, the concept of quasi boundary triple. Here, the authors of the paper under review develop the concept of quasi boundary triple and provide in an abstract setting conditions which ensure that the difference between the resolvents of two self adjoint extensions belong to certain classes of operators. The membership to such classes in cases of interest in the applications imply the validity of some information on the asymptotic behaviour of the corresponding singular values. Then the authors present several applications to the analysis of boundary value problems for elliptic operators in divergence form and for the Schrödinger operator with a potential supported in a \(C^{\infty}\) compact hypersurface.