4 papers
Weil asymptotic formula for the Laplacian on domains with rough boundaries
Yu. Netrusov, Yu. Safarov
We study asymptotic distribution of eigenvalues of the Laplacian on a bounded domain in . Our main results include an explicit remainder estimate in the Weyl formula for the…
Periodic points of quasianalytic Hamiltonian billiards
M. Novitskii, Yu. Safarov
We study absolutely periodic points and trajectories of Hamiltonian systems. Our main result is a necessary and sufficient for a Hamiltonian system to have the following property:…
Birkhoff's theorem and multidimensional numerical range
Yuri Safarov
We study the relation between the spectrum of a self-adjoint operator and its multidimensional numerical range. It turns out that the multidimensional numerical range is a convex s…
Fourier Tauberian Theorems and Applications
Y Safarov
The main aim of the paper is to present a general version of the Fourier Tauberian theorem for monotone functions. This result, together with Berezin's inequality, allows us to obt…