Left translates of a square integrable function on the Heisenberg group

• Autores: R. Radha, Saswata Adhikari
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 2, 2020, págs. 239-262
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.