Ground-state representation for fractional Laplacian on half-line

TL;DR

This paper provides a ground-state representation for the fractional Laplacian operator with Dirichlet boundary conditions on the half-line, advancing the mathematical understanding of fractional differential operators in constrained domains.

Contribution

It introduces a novel ground-state representation for the fractional Laplacian on the half-line with Dirichlet conditions, which was not previously established.

Findings

Derived explicit ground-state representation for fractional Laplacian

Enhanced understanding of boundary effects on fractional operators

Potential applications in boundary value problems involving fractional derivatives

Abstract

We give ground-state representation for the fractional Laplacian with Dirichlet condition on the half-line