Some Spectral Properties of the Non-self-adjoint Friedrichs Model Operator
نویسنده
چکیده
A non-self-adjoint, rank-one Friedrichs model operator in L2(R) is considered in the case where the determinant of perturbation is an outer function in the half-planes C±. Its spectral structure is investigated. The impact of the linear resolvent growth condition on its spectral properties (including the similarity problem) is studied.
منابع مشابه
Inverse Sturm-Liouville problems with a Spectral Parameter in the Boundary and transmission conditions
In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining a new Hilbert space and using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...
متن کاملOn Generalization of Sturm-Liouville Theory for Fractional Bessel Operator
In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...
متن کاملThe Wave Equation in Non-classic Cases: Non-self Adjoint with Non-local and Non-periodic Boundary Conditions
In this paper has been studied the wave equation in some non-classic cases. In the rst case boundary conditions are non-local and non-periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers,in which two ...
متن کاملSpectral Bounds Using Higher Order Numerical Ranges
We describe how to obtain bounds on the spectrum of a non-self-adjoint operator by means of what we call its higher order numerical ranges. We prove some of their basic properties and describe explain how to compute them. We finally use them to obtain new spectral insights into the non-selfadjoint Anderson model in one and two space dimensions. keywords: non-self-adjoint operator, spectrum, num...
متن کاملAsymptotic distribution of eigenvalues of the elliptic operator system
Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.
متن کامل