A. Sobolev

activity

20012022

most citedScaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof

87 citations · 337 across the 24 of their papers we have counts for

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Showing 2016 · math.SPShow all

4 papers · 2 filters

math.SP2016

Formulas of Szegő type for the periodic Schrödinger operator

Bernhard Pfirsch, Alexander V. Sobolev

We prove asymptotic formulas of Szegő type for the periodic Schrödinger operator $H = - \frac{d ^{2}}{d x ^{2}} + V$ in dimension one. Admitting fairly general functions $h$ with $h (0) = 0$ , we…

math.SP2016

Extreme eigenvalues of an integral operator

Alexander V. Sobolev

We study the family of compact operators $B_{α} = V A_{α} V$ , $α > 0$ in $L^{2} (R^{d})$ , $d \geq 1$ , where $A_{α}$ is the pseudo-differential operator with symbol $a_α(\boldsymbolξ) = a(…

math.SP2016★ 1 cited

Quasi-classical asymptotics for functions of Wiener-Hopf operators: smooth vs non-smooth symbols

Alexander V. Sobolev

We consider functions of Wiener--Hopf type operators on the Hilbert space $L^{2} (R^{d})$ . It has been known for a long time that the quasi-classical asymptotics for traces of r…

math.SP2016★ 2 cited

Trace formulas for Wiener--Hopf operators with applications to entropies of free fermionic equilibrium states

Hajo Leschke, Alexander V. Sobolev, Wolfgang Spitzer

We consider non-smooth functions of (truncated) Wiener--Hopf type operators on the Hilbert space $L^{2} (R^{d})$ . Our main results are uniform estimates for trace norms ($d\ge 1…