The Berezin and Garding Inequalities

Details The Berezin and Garding Inequalities The Berezin and Garding Inequalities

2005-12-22

arxiv.org/abs/math/0512512v1

Functional Analysis and Its Applications, 39, No. 4 (2005), 301-307

Mathematics

Spectral Theory

9pp

Scientific paper

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.

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