未决问题:具有复势的薛定谔算子的违反局域性问题

Jean-Claude Cuenin, Rupert L. Frank
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引用次数: 0

摘要

我们解释了具有复杂势的薛定谔算子在何种意义上出现了违反局域性(或韦尔渐近性)的现象,并提出了与这一现象相关的三个未决问题。
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Open problem: Violation of locality for Schrödinger operators with complex potentials
We explain in which sense Schr\"odinger operators with complex potentials appear to violate locality (or Weyl's asymptotics), and we pose three open problems related to this phenomenon.
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Uniform resolvent estimates, smoothing effects and spectral stability for the Heisenberg sublaplacian Topological and dynamical aspects of some spectral invariants of contact manifolds with circle action Open problem: Violation of locality for Schrödinger operators with complex potentials Arbitrarily Finely Divisible Matrices A review of a work by Raymond: Sturmian Hamiltonians with a large coupling constant -- periodic approximations and gap labels
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