Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

M -functions for Closed Extensions of Adjoint Pairs of Operators with Applications to Elliptic Boundary Problems

In this paper, we combine results on extensions of operators with recent results on the relation between the M -function and the spectrum, to examine the spectral behaviour of boundary value problems. M -functions are defined for general closed extensions, and associated with realisations of elliptic operators. In particular, we consider both ODE and PDE examples where it is possible for the op...

Principal Functions of Non-Selfadjoint Difference Operator with Spectral Parameter in Boundary Conditions

and Applied Analysis 3 for λ 2 cos z, where z ∈ : {z : z ∈ , Im z ≥ 0} and αn, Anm are expressed in terms of an and bn as

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...

Ela Vector and Operator Trapezoidal Type Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces∗

Some vector and operator generalized trapezoidal inequalities for continuous functions of selfadjoint operators in Hilbert spaces are given. Applications for power and logarithmic functions of operators are provided as well.