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Left translates of a square integrable function on the Heisenberg group
Collectanea Mathematica ( IF 0.7 ) Pub Date : 2019-06-17 , DOI: 10.1007/s13348-019-00255-4 R. Radha , Saswata Adhikari
Collectanea Mathematica ( IF 0.7 ) Pub Date : 2019-06-17 , DOI: 10.1007/s13348-019-00255-4 R. Radha , Saswata Adhikari
The aim of this paper is to study some properties of left translates of a square integrable function on the Heisenberg group. First, a necessary and sufficient condition for the existence of the canonical dual to a function \(\varphi \in L^{2}(\mathbb {R}^{2n})\) is obtained in the case of twisted shift-invariant spaces. Further, characterizations of \(\ell ^{2}\)-linear independence and the Hilbertian property of the twisted translates of a function \(\varphi \in L^{2}(\mathbb {R}^{2n})\) are obtained. Later these results are shown in the case of the Heisenberg group.
中文翻译:
海森堡群上平方可积函数的左平移
本文的目的是研究海森堡群上平方可积函数的左平移的一些性质。首先,在扭曲移位的情况下,获得了对函数\(\ varphi \ in L ^ {2}(\ mathbb {R} ^ {2n})\)的规范对偶的存在的充要条件-不变空间。此外,\(\ ell ^ {2} \)的线性独立性和函数\(\ varphi \ in L ^ {2}(\ mathbb {R} ^ {2n})的扭曲平移的希尔伯特性质的表征\)。后来,这些结果在海森堡小组中得到了证明。
更新日期:2019-06-17
中文翻译:
海森堡群上平方可积函数的左平移
本文的目的是研究海森堡群上平方可积函数的左平移的一些性质。首先,在扭曲移位的情况下,获得了对函数\(\ varphi \ in L ^ {2}(\ mathbb {R} ^ {2n})\)的规范对偶的存在的充要条件-不变空间。此外,\(\ ell ^ {2} \)的线性独立性和函数\(\ varphi \ in L ^ {2}(\ mathbb {R} ^ {2n})的扭曲平移的希尔伯特性质的表征\)。后来,这些结果在海森堡小组中得到了证明。