144 citations · 163 across the 8 of their papers we have counts for
4 papers · 1 filter
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…
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…
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 in with complex potential has absolute value at most a constant…
Eigenvalue bounds for Schrödinger operators with complex potentials
Rupert L. Frank
We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an…