L. Parnovski

collaborators

4 papers

math.SP2025

Perturbative diagonalization and spectral gaps of quasiperiodic operators on $ℓ^{2} (Z^{d})$ with monotone potentials

Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg

We obtain a perturbative proof of localization for quasiperiodic operators on $ℓ^{2} (Z^{d})$ with one-dimensional phase space and monotone sampling functions, in the regime of smal…

math.SP2025

On gaps in the spectra of quasiperiodic SchrÃ¶dinger operators with discontinuous monotone potentials

Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg

We show that, for one-dimensional discrete SchrÃ¶dinger operators, stability of Anderson localization under a class of rank one perturbations implies absence of intervals in spectr…

math-ph2025

Bethe-Sommerfeld Conjecture and Absolutely Continuous Spectrum of Multi-Dimensional Quasi-Periodic SchrÃ¶dinger Operators

Yulia Karpeshina, Leonid Parnovski, Roman Shterenberg

We consider SchrÃ¶dinger operators $H = - I^ + V (x)$ in $R^{d}$ , $d \geq 2$ , with quasi-periodic potentials $V (x)$ . We prove that the absolutely continuous spe…

math.SP2025

Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues

Michael Levitin, Leonid Parnovski, Iosif Polterovich +1

In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional…

Perturbative diagonalization and spectral gaps of quasiperiodic operators on ℓ2(Zd) with monotone potentials

On gaps in the spectra of quasiperiodic SchrÃ¶dinger operators with discontinuous monotone potentials

Bethe-Sommerfeld Conjecture and Absolutely Continuous Spectrum of Multi-Dimensional Quasi-Periodic SchrÃ¶dinger Operators

Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues

Perturbative diagonalization and spectral gaps of quasiperiodic operators on $ℓ^{2} (Z^{d})$ with monotone potentials