5 citations · 11 across the 12 of their papers we have counts for
12 papers
Lower bounds for the counting function of integral operators
Yuri Safarov
The paper presents a lower bound for the number of negative eigenvalues of an integral operator with continuous kernel K lying below a nonpositive number t. The estimate is given i…
A symbolic calculus for Fourier integral operators
Yuri Safarov
The paper develops a symbolic calculus for Fourier integral operators associated with canonical transformations.
The semiclassical theory of discontinuous systems and ray-splitting billiards
Dmitry Jakobson, Yuri Safarov, Alexander Strohmaier +1
We analyze the semiclassical limit of spectral theory on manifolds whose metrics have jump-like discontinuities. Such systems are quite different from manifolds with smooth Riemann…
Pseudodifferential operators on manifolds: a coordinate-free approach
P. Mckeag, Y. Safarov
This is a review of some coordinate-free calculi of pseudodifferential operators developed in the last years. As an application, we use a coordinate-free calculus to obtain new res…
On the relation between an operator and its self-commutator
N. Filonov, Y. Safarov
Our main result is a theorem saying that a bounded operator on a Hilbert space belongs to a certain set associated with its self-commutator , provided that can…
On the comparison of the Dirichlet and Neumann counting functions
Y. Safarov
The aim of the paper is to show that L. Friedlander's results on the relation between Dirichlet and Neumann counting functions (Arch. Ration. Mech. Anal. 116, 1991) remain valid in…