Rupert L. Frank

activity

20152025

most citedEigenvalue bounds for Schrödinger operators with complex potentials. II

1 citations · 1 across the 4 of their papers we have counts for

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math.SP2025

Eigenvalue lower bounds through a generalized inradius

Rupert L. Frank, Ari Laptev, Durvudkhan Suragan

Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for ei…

math.SP2024

Open problem: Violation of locality for Schrödinger operators with complex potentials

Jean-Claude Cuenin, Rupert L. Frank

We explain in which sense Schrödinger operators with complex potentials appear to violate locality (or Weyl's asymptotics), and we pose three open problems related to this phenomen…

math.SP2015★ 1 cited

Eigenvalue bounds for Schrödinger operators with complex potentials. II

Rupert L. Frank, Barry Simon

Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator $- Δ + V$ in $L^{2} (R^{ν})$ with complex potential has absolute value at most a constant…