四元数Segal-Bargmann变换的映射性质
The Mapping Properties of the Quaternionic Segal-Bargmann Transform on
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。
Abstract:
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.
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