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
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• 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 φ∈L2(R2n) is obtained in the case of twisted shift-invariant spaces. Further, characterizations of ℓ2-linear independence and the Hilbertian property of the twisted translates of a function φ∈L2(R2n) are obtained. Later these results are shown in the case of the Heisenberg group.