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math.SP2017★ 11 cited
Self-adjoint and skew-symmetric extensions of the Laplacian with singular Robin boundary condition
Sergei A. Nazarov, Nicolas Popoff
We study the Laplacian in a smooth bounded domain, with a varying Robin boundary condition singular at one point. The associated quadratic form is not semi-bounded from below, and…
math.SP2017
Criteria for the Absence and Existence of Bounded Solutions at the Threshold Frequency in a Junction of Quantum Waveguides
Fedor L. Bakharev, Sergei A. Nazarov
In the junction of several semi-infinite cylindrical waveguides we consider the Dirichlet Laplacian whose continuous spectrum is the ray with a positive…