The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions
Journal: Sahand Communications in Mathematical Analysis (Vol.10, No. 1)Publication Date: 2018-04-01
Authors : Leila Nasiri; Ali Sameripour;
Page : 37-46
Keywords : Resolvent; Distribution of eigenvalues; Non-selfadjoint differential operators;
Abstract
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 estimate the resolvent of the operator $L$ on the one-dimensional space $ L_{2}(Omega)$ using some analytic methods.
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