SPECTRAL PROPERTIES AND DISTRIBUTION OF EIGENVALUES OF NON–SELF-ADJOINT ELLIPTIC DIFFERENTIAL OPERATORS

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

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

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

Eigenvalues in Spectral Gaps of Differential Operators

Spectral problems with band-gap spectral structure arise in numerous applications, including the study of crystalline structure and the determination of transmitted frequencies in photonic waveguides. Numerical discretization of these problems can result in spurious results, a phenomenon known as spectral pollution. We present a method for calculating eigenvalues in the gaps of self-adjoint ope...