Bitriangular Operators of Jordan form and Inverse Spectral Theory for Symmetric Operators on Joint Invariant Subspaces

Abstract

We show the sum rules and their applications of special form for Jacobi matrices, and the spectral properties of self-adjoint extensions of Weyl functions are considered. The representation and Jordan form of biquasitriangular operators are studied, and we determined the homogeneous shift with operators on Hilbert spaces and, also show the inverse spectral theory for symmetric operators with several gaps. We obtained the characteristic operator function of the class of n-hypercontractions on joint invariant subspaces.