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
• DOI: 10.1007/s13348-019-00255-4
• 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 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.

• Referencias bibliográficas
  • Barbieri, D., Hernandez, E., Mayeli, A.: Bracket map for the Heisenberg group and the characterization of cyclic subspaces. Appl. Comput....
  • Barbieri, D., Hernandez, E., Parcet, J.: Riesz and frame systems genarated by unitary actions of discrete groups. Appl. Comput. Harmon. Anal....
  • Bownik, M.: The structure of shift-invariant subspaces of $$L^{2}(\mathbb{R}^{n})$$ L 2 ( R n ) . J. Funct. Anal. 176, 282–309...
  • Cabrelli, C., Paternostro, V.: Shift-invariant spaces on LCA groups. J. Funct. Anal. 258, 2034–2059 (2010)
  • Christensen, O.: Frames and Bases an Introductory Course. Birkhäuser, Boston (2008)
  • Currey, B., Mayeli, A., Oussa, V.: Characterization of shift-invariant spaces on a class of Nilpotent Lie groups with application. J. Fourier...
  • Heil, C.: A Basis Theory Primer. Birkhäuser, Basel (2011)
  • Hernandez, E., Sikic, H., Weiss, G., Wilson, E.: On the Properties of the Integer Translates of a Square Integrable Function in $$L^{2}({\mathbb{R}})$$ L 2 ( R ) ,...
  • Iverson, J.: Frames generated by compact group actions. Trans. Am. Math. Soc. 370(1), 509–551 (2018)
  • Kamyabi Gol, R.A., Raisi Tousi, R.: The structure of shift invariant spaces on a locally compact abelian group. J. Math. Anal. Appl. 340,...
  • Kislyakov, S.V.: A sharp correction theorem. Studia Math. 113(2), 177–196 (1995)
  • Radha, R., Adhikari, S.: Frames and Riesz bases of twisted shift-invariant spaces in $$L^{2}(\mathbb{R}^{2n})$$ L 2 ( R 2 n ) ....
  • Radha, R., Adhikari, S.: Shift-invariant spaces with countably many mutually orthogonal generators on the Heisenberg group. arXiv:1711.06902 ...
  • Radha, R., Shravan kumar, N.: Shift-invariant subspaces on compact groups. Bull. Sci. Math 137(No 4), 485–497 (2013)
  • Luef, F.: Projections in noncommutative tori and Gabor frames. Proc. Am. Math. Soc. 139, 571–582 (2011)
  • Saliani, S.: $$\ell ^{2}$$ ℓ 2 -linear independence for the system of integer translates of a square integrable function. Proc. Am....
  • Thangavelu, S.: Harmonic Analysis on the Heisenberg Group. Birkhäuser, Boston (1997)