Dirichlet Fractional Laplacian in multi-tubes

TL;DR

This paper investigates the spectral properties of the Dirichlet fractional Laplacian in multi-tube domains with cylindrical outlets, revealing new effects compared to the classical local case and providing improved theoretical results.

Contribution

It introduces a detailed analysis of the spectrum for the fractional Laplacian in multi-tube domains and presents significant improvements to existing theorems.

Findings

Discovery of new spectral effects in multi-tube domains

Enhanced understanding of the fractional Laplacian's spectrum

Improved version of Theorem 4

Abstract

We describe the spectrum structure for the restricted Dirichlet fractional Laplacian in multi-tubes, i.e. domains with cylindrical outlets to infinity. Some new effects in comparison with the local case are discovered. In this version, Theorem 4 is essentially improved.