A. V. Sobolev

activity

20102026

most citedOn a coefficient in trace formulas for Wiener-Hopf operators

3 citations · 3 across the 2 of their papers we have counts for

collaborators

6 papers

math-ph2026

Eigenvalue asymptotics for the one-particle density matrix and one-particle kinetic energy density operator

Søren Fournais, Alexander V. Sobolev

Let $ψ (x)$ , $x \in R^{3 N}$ , be an eigenfunction of the $N$ -particle atomic Schrödinger operator. We consider the one-particle density matrix $γ (x, y)$ …

math.SP2016★ 3 cited

On a coefficient in trace formulas for Wiener-Hopf operators

A. V. Sobolev

Let $a = a (ξ), ξ \in R,$ be a smooth function quickly decreasing at infinity. For the Wiener-Hopf operator $W (a)$ with the symbol $a$ , and a smooth function $g:\mathbb C\to~\…

math.SP2013

On the spectrum of an "even" periodic Schroedinger operator with a rational magnetic flux

N. D. Filonov, A. V. Sobolev

We study the Schrödinger operator on $L_{2} (R^{3})$ with periodic variable metric, and periodic electric and magnetic fields. It is assumed that the operator is reflection symm…

math.SP2011

On Hankel-type operators with discontinuous symbols in higher dimensions

A. V. Sobolev

We obtain an asymptotic formula for the counting function of the discrete spectrum for Hankel-type pseudo-differential operators with discontinuous symbols.

math.SP2011

A family of anisotropic integral operators and behaviour of its maximal eigenvalue

B. S Mityagin, A. V. Sobolev

We study the family of compact integral operators $K_{β}$ in $L^{2} (R)$ with the kernel K_β(x, y) = \frac{1}π\frac{1}{1 + (x-y)^2 + β^2Θ(x, y)}, depending on the parame…

math.SP2010

Quasi-classical asymptotics for pseudo-differential operators with discontinuous symbols: Widom's Conjecture

Alexander V. Sobolev

Relying on the known two-term quasiclassical asymptotic formula for the trace of the function $f (A)$ of a Wiener-Hopf type operator $A$ in dimension one, in 1982 H. Widom conjectur…