四元数Segal-Bargmann变换的 L p 映射性质  

The Mapping Properties of the Quaternionic Segal-Bargmann Transform on L p

作　　者：韩媛媛 

机构地区：[1]天津师范大学数学科学学院,天津

出　　处：《理论数学》2024年第6期331-340,共10页Pure Mathematics

摘　　要：本文研究了四元数Segal-Bargmann变换的Lp映射性质。具体来说,当2 < p≤∞时,该变换是从四元数值函数空间Lp(ℝ;ℍ)到四元数Bargmann-Fock空间ℱslicep,ν(ℍ)的有界线性算子并且是单射;当1≤p < 2时,该变换是从Lp(ℝ;ℍ)到ℱslicep′,ν(ℍ)的有界算子但不是Lp(ℝ;ℍ)到ℱslicep,ν(ℍ)的有界算子,其中1/p+1/p′=1。In this paper, we study the mapping properties of the quaternionic Segal-Bargmann transform onLp. To be specific, when2 < p≤∞, the transform is a bounded operator from quaternionic numerical function spaceLp(ℝ;ℍ)to the quaternionic Bargmann-Fock spaceℱslicep,ν(ℍ), and this operator is injective. When1≤p < 2, the transform is a bounded operator fromLp(ℝ;ℍ)toℱslicep′,ν(ℍ)but it not mapsLp(ℝ;ℍ)boundedly into theℱslicep,ν(ℍ), where1/p+1/p′=1.

关 键 词：FOCK空间 四元数 Segal-Bargmann变换 切片正则函数 

分 类 号：O17[理学—数学]