Fractional Laplacian in V-shaped waveguide

Abstract

The spectral properties of the restricted fractional Dirichlet Laplacian in V-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray $[{\Lambda }_{†},+\infty )$ with the threshold corresponding to the smallest eigenvalue of the cross-sectional problems. In this work, the presence of a discrete spectrum at any junction angle is established along with the monotonic dependence of the discrete spectrum on the angle.