Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels

Abstract

Motivated by the study of relativistic atoms, we consider the Hardy operator $(-\Delta {)}^{\alpha /2}-\kappa |x{|}^{-\alpha }$ acting on functions of the form $u(|x|)|x{|}^{\ell }{Y}_{\ell ,m}(x/|x|)$ in $L^2({\mathbb{R}}^d)$, when $\kappa \ge 0$ and $\alpha \in (0,2]\cap (0,d+2\ell )$. We give a ground state representation of the corresponding form on the half-line (Theorem 1.5). For the proof we use subordinated Bessel heat kernels.

arXiv comment32 pages

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Cited by in corpus (1)

• Subordinated Bessel heat kernels