Abstract
We establish different estimates for the sums of negative eigenvalues of elliptic operators. Our proofs are based on a property of the eigenvalue sums that might be viewed as a certain convexity with respect to the perturbation.
Highlights
We study the negative eigenvalues λ j of the operator H
Pn where the minimum is taken over all possible orthogonal projections Pn of rank n that have the property Ran Pn ⊂ D(H )
This eigenvalue was studied in the proof of Theorem 1.4, according to which λ1 → γ [α] as → 0
Summary
We study the negative eigenvalues λ j of the operator H . Let V1 and V2 be two positive selfadjoint operators, such that Let A be the selfadjoint operator in L2(Rd ) defined by A = (− )l , 2l > d, and let V be the operator of multiplication by a positive function V (x) ≥ 0.
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