The Berezin and Garding Inequalities
Spectral Theory
2007-05-23 v1
Abstract
Let F be a real-valued convex function on the complex plane, and let Ps(b) be a pseudodifferential operator with symbol b. Under certain natural assumptions about properties of pseudodifferential operators, we prove that the sum of F(z) over all eigenvalues z of the operator Ps(b) counted with their multiplicities does not exceed the real part of the trace of Ps(F(b)) modulo a term of the same order as the error term in the Garding inequality.
Cite
@article{arxiv.math/0512512,
title = {The Berezin and Garding Inequalities},
author = {Y. Safarov},
journal= {arXiv preprint arXiv:math/0512512},
year = {2007}
}
Comments
9pp