Hilbert space valued Gabor frames in weighted amalgam spaces

Anirudha Poria, Jitendriya Swain*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let H be a separable Hilbert space. In this paper, we establish a generalization of Walnut's representation and Janssen's representation of the H-valued Gabor frame operator on H-valued weighted amalgam spaces WH(Lp, Lqv ), 1 ≤ p, q ≤ ∞. Also, we show that the frame operator is invertible on WH(Lp, Lqv ), 1 ≤ p, q ≤ ∞, if the window function is in the Wiener amalgam space WH(L∞, L1 w). Further, we obtain the Walnut representation and invertibility of the frame operator corresponding to Gabor superframes and multiwindow Gabor frames on WH(Lp, Lqv ), 1 ≤ p, q ≤ ∞, as a special case by choosing the appropriate Hilbert space H.

Original languageEnglish
Pages (from-to)377-394
Number of pages18
JournalAdvances in Pure and Applied Mathematics
Issue number4
Publication statusPublished - 1 Oct 2019


  • Amalgam spaces
  • Gabor expansions
  • Gabor frames
  • Sampling
  • Superframes
  • Time-frequency analysis
  • Walnut representation
  • Wexler-Raz biorthogonality
  • Wiener's Lemma


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