We use a “weakly formulated” Sylvester equation H1/2TM−1/2 −H−1/2TM1/2 = F to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known results of Davis and Kahan. Another application is a bound for the square root of a positive selfadjoint operator which extends the known rule: “The relative error in the squar...

The representations of the degenerate affine Hecke algebra in which the analogues of the Dunkl operators are given by finite-difference operators are introduced. The non-selfadjoint lattice analogues of the spin Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The sl(m)-Yangian representations arising from the finite-difference representations of the degenerate affine Hecke algebr...

We construct efficient approximations for the eigenfunctions of non-selfadjoint Schrödinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrödinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable ad...

The paper is a continuation of Part I and contains several further results on generalized boundary triples, the corresponding Weyl functions, applications this technique to ordinary partial differential operators. We establish connection between Post's theory pairs closed nonnegative forms one hand triples symmetric operators other hand. Applications Laplacian operator bounded domains with smoo...

We consider the analytic continuation of the transfer function associated with a 2×2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We construct a family of non-selfadjoint operators which factorize the transfer function and reproduce certain parts of its spectrum including the nonreal (resonance) spectrum situated in the unphysical sheets neighboring ...

Some recent inequalities for the Čebyšev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are surveyed.