3 papers
math.SP2026
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 o…
math.SP2026
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 a…
math.CA2024
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…