Sums of Regular Selfadjoint Operators

Error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems

We consider elliptic operators A on a bounded domain, that are compact perturbations of a selfadjoint operator. We first recall some spectral properties of such operators: localization of the spectrum and resolvent estimates. We then derive a spectral inequality that measures the norm of finite sums of root vectors of A through an observation, with an exponential cost. Following the strategy of...

The Horn Conjecture for Sums of Compact Selfadjoint Operators

We determine the possible nonzero eigenvalues of compact selfadjoint operators A, B(1), B(2), . . ., B(m) with the property that A = B(1) +B(2) +· · ·+B(m). When all these operators are positive, the eigenvalues were known to be subject to certain inequalities which extend Horn’s inequalities from the finite-dimensional case when m = 2. We find the proper extension of the Horn inequalities and ...

Dilations‎, ‎models‎, ‎scattering and spectral problems of 1D discrete Hamiltonian systems

In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...