Fractional Laplacian in V-shaped waveguide

Abstract

The spectral properties of the restricted fractional Dirichlet Laplacian in $\mathsf{V}$-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray $[\hat{I}{›}_{†},+\infty )$ 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.

13 pages, 1 figure