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math.SP2025
Perturbative diagonalization and spectral gaps of quasiperiodic operators on with monotone potentials
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
We obtain a perturbative proof of localization for quasiperiodic operators on with one-dimensional phase space and monotone sampling functions, in the regime of smal…
math.SP2025
On gaps in the spectra of quasiperiodic Schrödinger operators with discontinuous monotone potentials
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
We show that, for one-dimensional discrete Schrödinger operators, stability of Anderson localization under a class of rank one perturbations implies absence of intervals in spectr…
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…