We derive inequalities for sums of eigenvalues of Schrödinger operators on finite intervals and tori. In the first of these cases, the inequalities converge to the classical trace formulae in the limit as the number of eigenvalues considered approaches infinity.
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Pedro Freitas, James B. Kennedy, Summation formula inequalities for eigenvalues of Schrödinger operators. J. Spectr. Theory 6 (2016), no. 3, pp. 483–503DOI 10.4171/JST/130