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

IF 2.1 1区 数学 Q1 MATHEMATICS
Krzysztof Bogdan , Konstantin Merz
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引用次数: 0

Abstract

Motivated by the study of relativistic atoms, we consider the Hardy operator (Δ)α/2κ|x|α acting on functions of the form u(|x|)|x|Y,m(x/|x|) in L2(Rd), when κ0 and α(0,2](0,d+2). 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.

角动量通道中带有哈代势能的分数拉普拉斯基态表示法
受相对论原子研究的启发,我们考虑哈代算子在 、 和 时作用于形式为 的函数。我们给出了相应形式的基态在右半边的表示(定理 1.5)。为了证明这一点,我们使用了从属贝塞尔热核。
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来源期刊
CiteScore
4.30
自引率
0.00%
发文量
84
审稿时长
6 months
期刊介绍: Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.
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