Localization operators on discrete modulation spaces

Aparajita Dasgupta, Anirudha Poria*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this paper, we study a class of pseudo-differential operators known as time-frequency localization operators on Zn , which depend on a symbol ς and two windows functions g1 and g2 . We define the short-time Fourier transform on Zn× Tn and modulation spaces on Zn , and present some basic properties. Then, we use modulation spaces on Zn× Tn as appropriate classes for symbols, and study the boundedness and compactness of the localization operators on modulation spaces on Zn . Then, we show that these operators are in the Schatten–von Neumann class. Also, we obtain the relation between the Landau–Pollak–Slepian type operator and the localization operator on Zn . Finally, under suitable conditions on the symbols, we prove that the localization operators are paracommutators, paraproducts and Fourier multipliers.

Original languageEnglish
Article number59
JournalBanach Journal of Mathematical Analysis
Issue number3
Publication statusPublished - Jul 2023


  • Compact operators
  • Discrete modulation spaces
  • Fourier multipliers
  • Localization operators
  • Paracommutators
  • Paraproducts
  • Schatten–von Neumann class
  • Short-time Fourier transform


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