• Corpus ID: 246652199

Spectral asymptotics for the fourth-order operator with periodic coefficients

  title={Spectral asymptotics for the fourth-order operator with periodic coefficients},
  author={Dmitry M. Polyakov},
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. 
1 Citations
Linear differential operators with distribution coefficients of various singularity orders
. In this paper, the linear differential expression of order n ≥ 2 with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of


Spectral Estimates for the Fourth-Order Operator with Matrix Coefficients
The fourth-order differential operator with matrix coefficients with the domain determined by quasi-periodic boundary conditions is considered. For this operator, the asymptotics of the arithmetic
Spectral properties of an even-order differential operator
We present the spectral properties of an even-order differential operator whose domain is described by periodic and antiperiodic boundary conditions or the Dirichlet conditions. We derive an
Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients
Using the method of similar operators, we study the spectral properties of a fourth-order differential operator with two types of classical boundary conditions. We obtain asymptotics for the spectrum
Third-order operators with three-point conditions associated with Boussinesq's equation
We consider a non-self-adjoint third-order operator on the interval with real 1-periodic coefficients and three-point Dirichlet conditions at the points 0, 1 and 2. The eigenvalues of this operator
Asymptotics of the spectrum of nonsmooth perturbations of differential operators of order 2m
On a finite closed interval, we obtain the asymptotics of the eigenvalues of a differential operator of order 2m perturbed by a differential operator of order 2m − 2 given by a quasidifferential
Let m 2 N, � 2 (0,1), and V be a 1-periodic complex-valued distribution in the negative Sobolev space H m� (0,1). The singular non-self-adjoint eigenvalue problem D 2m u + V u = �u, D = id/dx, with
Trace formula for fourth order operators on the circle
We determine the trace formula for the fourth order operator on the circle. This formula is similar to the famous trace formula for the Hill operator obtained by Dubrovin, Its-Matveev and McKean-van
Eigenvalue and Eigenfunction Asymptotics for Regular Sturm-Liouville Problems
Abstract In this paper, we obtain asymptotic formulas for eigenvalues, eigenfunctions, and the reciprocals of the eigenfunction norms for eigenvalue problems associated with the general
Spectrum of periodic elliptic operators with distant perturbations in space
A periodic selfadjoint differential operator of even order and with distant perturbations in a multidimensional space is treated. The role of perturbations is played by arbitrary localized operators.