Related papers: On the Spectrality of the Differential Operators w…
In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.
In this paper we investigate the spectral expansion for the asymptotically spectral differential operators generated in all real line by ordinary differential expression of arbitrary order with periodic matrix-valued coefficients
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
In this paper we investigate the spectrum of the differential operators generated by the ordinary differential expression of odd order with PT-symmertic periodic matrix coefficients
In this paper we construct the spectral expansion for the differential operator generated in all real line by ordinary differential expression of arbitrary order with periodic complex-valued coefficients by introducing new concepts as…
Partial operators can have void or unbounded spectra. Contrarily to what is written in Dunford-Schwarz, the reason is not in the fact they are unounded operators.
It is shown that the nonselfadjoint (and non-normal) linear ordinary differential operators of a certain class are spectral operators of scalar type in the sense of Dunford and Bade. Operators of this kind appear in physical problems such…
We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral…
Ordinary differential operators with periodic coefficients analytic in a strip act on a Hardy-Hilbert space of analytic functions with inner product defined by integration over a period on the boundary of the strip. Simple examples show…
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…
Finiteness of the point spectrum of linear operators acting in a Banach space is investigated from point of view of perturbation theory. In the first part of the paper we present an abstract result based on analytical continuation of the…
In this paper we present how spectral properties of certain linear operators vary when operators are considered in different Hilbert spaces having common dense domain as the space of polynomials in one real variable with complex…
For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…
In this paper, we study the spectrality of the non-self-adjoint Dirac operator L(Q) with a complex-valued periodic matrix potential Q. We establish a condition on the off-diagonal elements of the matrix Q under which L(Q) is an…
In this paper we construct the spectral expansion for the non-self-adjoint differential operators generated in the space of vektor functions by the ordinary differential expression of arbitrary order with the periodic matrix coefficients by…
We consider the self-adjoint fourth-order operator with real $1$-periodic coefficients on the unit interval. The spectrum of this operator is discrete. We determine the high energy asymptotics for its eigenvalues.
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…
We consider $2p\ge 4$ order differential operator on the real line with a periodic coefficients. The spectrum of this operator is absolutely continuous and is a union of spectral bands separated by gaps. We define the Lyapunov function,…