Some properties of Riesz potential associated with SchrSdinger operator

Let L = −Δ + V be the Schr?dinger operator on ℝ ^d , d ≥ 3, where Δ is the Laplacian on ℝ ^d and V ≢ 0 is a nonnegative function satisfying the reverse H?lder inequality. In this article, the author investigates some properties of the Riesz potential I _α ^L associated with L on the Campanato-type spaces Λ _L ^β and the Hardy-type spaces H _L ^p .     

Calculation of eigenvalues of a discrete self-adjoint operator perturbed by a bounded operator

We generalize the method of regularized traces which calculates eigenvalues of a perturbed discrete operator for the case of an arbitrary multiplicity of eigenvalues of the unperturbed operator. We obtain a system of equations, enabling one to calculate eigenvalues of the perturbed operator with large ordinal numbers. As an example, we calculate eigenvalues of a perturbed Laplace operator in a rectangle.     

Asymptotic behavior of the singular values of a generalization of the operator fractional integration

In this paper we find the first term in the asymptotics of singular values of the generalized fractional integration operator.     

Some properties of Riesz potential associated with Schr(O)dinger operator

Let (L) =-△ + V be the Schr(o)dinger operator on Rd,d ≥ 3,where △ is the Laplacian on Rd and V （≠） 0 is a nonnegative function satisfying the reverse H(O)lder inequality.In this article,the author inve...     

Spectral analysis of an impulsive quantum difference operator

This paper studies spectral analysis and symmetries of quantum difference equations of second order together with an impulsive condition. By determining a transfer matrix, we investigate the locations of the eigenvalues and spectral singularities of an operator corresponding to the q‐difference equation.     

Regularized traces of a perturbed laplace-beltrami operator on the unit two-dimensional sphere

The paper contains formulas for regularized traces of the Laplace-Beltrami operator on the unit sphere under perturbation determined by a bounded complex-valued potential and a sufficiently complete justification of these formulas. Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 702–705, May, 2000.     

Riesz potential operator in continual variable exponents Herz spaces

We find conditions on the variable parameters $p\left(x\right),q\left(t\right)$ and $\alpha \left(t\right)$, defining the Herz space $H^{p(·),q(·),\alpha (·)}\left({\mathbb{R}}^n\right)$, for the validity of Sobolev type theorem for the Riesz potential operator to be bounded within the frameworks of such variable exponents Herz spaces. We deal with a “continual” version of Herz spaces (which coincides with the “discrete” one when q is constant).     

Spectral properties of operator logarithms

We prove that the spectral height of the logarithm log A of a sectorial operator A equals the spectral angle of A. This yields old results of Prüss/Sohr and McIntosh as corollaries. Then we construct a sectorial operator A on a UMD space having bounded imaginary powers such that the group type of (A ^is ) _s is strictly greater than . Mathematics Subject Classification (2000):47A60,47D06.     

The second regularized trace of differential operator equation with the semi‐periodic boundary conditions

In this paper, we have obtained the second regularized trace formula for the differential operator equation with the semi‐periodic boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

A trace formula of a boundary value problem for the operator Sturm-Liouville equation

We obtain a regularized trace formula for the operator Sturm-Liouville equation with a boundary condition depending on a spectral parameter.     

Spectral properties of cosine operator functions

LetA be the generator of a cosine functionC _t ,t R in a Banach spaceX; we shall connect the existence and uniqueness of aT-periodic mild solution of the equationu = Au + f with the spectral property 1 (C _T ) and, in caseX is a Hilbert space, also with spectral properties ofA. This research was supported in part by DAAD, West Germany.     

Spectral properties of a Sturm-Liouville type differential operator with a retarding argument

Spectral properties of a differential operator of Sturm-Liouville type are studied in the case of retarding argument with different boundary conditions. The asymptotics of solutions to the corresponding differential equation is studied in the case of a summable potential. An asymptotics of eigenvalues and an asymptotics of eigenfunctions of the differential operator are calculated for each considered case.     

Spectral properties of the nonstationary two-dimensional Dirac operator

We study the self-adjointness and spectral structure of general first-order partial differential operators (including the nonstationary two-dimensional Dirac operator) and the structure of the resolvent of the two-dimensional Dirac operator.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 593–599, May, 1995.This work was partially supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology.