On the Finiteness of the Number of Eigenvalues of Jacobi Operators below the Essential Spectrum

On the Number of Eigenvalues of Jacobi Operators

We present a new oscillation criterion to determine whether the number of eigenvalues below the essential spectrum of a given Jacobi operator is finite or not. As a special case we obtain a generalization of Kenser’s criterion for Sturm-Liouville operators to Jacobi operators.

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

Oscillation Theory and Renormalized Oscillation Theory for Jacobi Operators

We provide a comprehensive treatment of oscillation theory for Jacobi operators with separated boundary conditions. Our main results are as follows: If u solves the Jacobi equation (Hu)(n) = a(n)u(n + 1) + a(n − 1)u(n − 1) − b(n)u(n) = λu(n), λ ∈ R (in the weak sense) on an arbitrary interval and satisfies the boundary condition on the left or right, then the dimension of the spectral projectio...

Spectrum and essential spectrum of linear combinations of composition operators on the Hardy space H2

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....

Self-commutators of composition operators with monomial symbols on the Bergman space

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...