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<p>We study the spatial decay behaviour of resolvent kernels for a large class of non-local Lévy operators and bound states of the corresponding Schrödinger operators. Our findings naturally lead us to proving results for Lévy measures, which have subexponential or exponential decay, respectively. This leads to sharp transitions in the decay rates of the resolvent kernels. We obtain estimates that allow us to describe and understand the intricate decay behaviour of the resolvent kernels and the bound states in either regime, extending findings by Carmona, Masters and Simon for fractional Laplacians (the subexponential regime) and relativistic operators (the exponential regime). Our proofs are mainly based on methods from the theory of operator semigroups.</p>

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Decay of resolvent kernels and Schrödinger eigenstates for Lévy operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月3日

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  • Kamil Kaleta,
  • René L. Schilling,
  • Paweł Sztonyk

摘要

We study the spatial decay behaviour of resolvent kernels for a large class of non-local Lévy operators and bound states of the corresponding Schrödinger operators. Our findings naturally lead us to proving results for Lévy measures, which have subexponential or exponential decay, respectively. This leads to sharp transitions in the decay rates of the resolvent kernels. We obtain estimates that allow us to describe and understand the intricate decay behaviour of the resolvent kernels and the bound states in either regime, extending findings by Carmona, Masters and Simon for fractional Laplacians (the subexponential regime) and relativistic operators (the exponential regime). Our proofs are mainly based on methods from the theory of operator semigroups.