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Trace Formulas for Schrödinger Operators on a Lattice

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Abstract

We consider Schrödinger operators with complex decaying potentials (in general, not of trace class) on a lattice. We determine trace formulas in terms of the eigenvalues and the singular measure and some integrals of a Fredholm determinant. The proof is based on estimates of the free resolvent and analysis of functions in Hardy spaces. Moreover, we obtain an estimate for eigenvalues and singular measure in terms of potentials.

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Acknowledgments

EK is grateful to A. Alexandrov (St. Petersburg) and K. Dyakonov (Barcelona) for useful comments about Hardy spaces.

Funding

Our study was supported by the RSF grant No. 19-71-30002.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    E. L. Korotyaev

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  1. E. L. Korotyaev
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Correspondence to E. L. Korotyaev.

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Korotyaev, E.L. Trace Formulas for Schrödinger Operators on a Lattice. Russ. J. Math. Phys. 29, 542–557 (2022). https://doi.org/10.1134/S1061920822040112

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