11 citations · 14 across the 5 of their papers we have counts for
5 papers
Pólya's conjecture for higher-dimensional Neumann balls
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
We prove Pólya's conjecture for the Neumann eigenvalues of the Laplacian on Euclidean balls in dimensions three and higher. The proof further develops the approach introduced in ou…
Pólya's conjecture for Dirichlet eigenvalues of annuli
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks an…
Uniform enclosures for the phase and zeros of Bessel functions and their derivatives
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel…
Inequalities à la Pólya for the Aharonov--Bohm eigenvalues of the disk
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
We prove an analogue of Pólya's conjecture for the eigenvalues of the magnetic Schrödinger operator with Aharonov--Bohm potential on the disk, for Dirichlet and magnetic Neumann bo…
Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons
Michael Levitin, Leonid Parnovski, Iosif Polterovich +1
We obtain asymptotic formulae for the Steklov eigenvalues and eigenfunctions of curvilinear polygons in terms of their side lengths and angles. These formulae are quite precise: th…