Subscalar Operators and Growth of Resolvent

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

ON p-HYPONORMAL OPERATORS

In this paper we show that p-hyponormal operators with 0 / ∈ σ(|T | 1 2 r ) are subscalar. As a corollary, we get that such operators with rich spectra have non-trivial invariant subspaces.

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

Complex Powers of Nondensely Defined Operators

The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...

On the Classiication of the Spectrum of Second Order Diierence Operators

We study nonsymmetric second order diierence operators acting in the Hilbert spacè 2 and describe the resolvent set and the essential spectrum of such operators in terms of related formal orthogonal polynomials. As an application, we obtain new results on the growth of orthonormal polynomials outside and inside the support of the underlying measure of orthogonality.