SIMPLE ESTIMATES OF THE DISCRETE SPECTRUM MULTIPLICITY FOR A CYLINDRICAL QUANTUM WAVEGUIDE WITH A RESONATOR
S.A. Nazarov
Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia
Keywords: quantum waveguide, Dirichlet problem for the Laplace operator, discrete spectrum, continuous spectrum
Abstract
For a multidimensional quantum waveguide with a cylindrical outlet at infinity, various upper and lower bounds on the multiplicity of its discrete spectrum are presented. Some estimates based on the eigenvalues of the integral-differential problem on a resonator are absent from the literature. At the same time, the problem under consideration makes it possible to obtain a sharper sufficient condition for nonemptiness of the discrete spectrum of the waveguide and an estimate of its multiplicity.
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