arXiv subjects

Dmitry M. Polyakov

Publications and source records attributed to Dmitry M. Polyakov.

3 recordsLinked to original sources

arXiv2026

Spectral asymptotics for two-term even-order differential operators with homogeneous delay

We consider two-term even-order operators on the unit interval with homogeneous delay and with Dirichlet and Neumann boundary conditions. The main result provides to the eigenvalue asymptotics of this operator with respect to all indices enumerating the eigenvalues. This asymptotic formula is uniform in the parameter of the homogeneous delay. We also discuss the nontrivial high-frequency phenomenon demonstrated by the uniform spectral asymptotics.

math.SP↗

arXiv2022

Spectral asymptotics for the fourth-order operator with periodic coefficients

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.

math.SP↗

arXiv2018

Spectral analysis of an even order differential operator

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 decompositions and spectral projections. We also establish the asymptotic behavior of the corresponding analytic semigroup of operators.

math.SP↗