On the principal eigenvalue of elliptic operators in R and applications

A Perron-type Theorem on the Principal Eigenvalue of Nonsymmetric Elliptic Operators

We provide a proof for a Perron-type theorem on the principal eigenvalue of nonsymmetric elliptic operators based on the strong maximum principle. This proof is modeled after a variational proof of Perron’s theorem for matrices with positive entries that does not appeal to Perron-Frobenius theory.

On convergence of sample and population Hilbertian functional principal components

In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains

Using three different notions of generalized principal eigenvalue of linear second order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the existence of positive eigenfunctions satisfying Dirichlet boundary conditions. Relations between these principal eigenvalues, their simplicity and several othe...

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