TY - JOUR
T1 - Localization operators on discrete modulation spaces
AU - Dasgupta, Aparajita
AU - Poria, Anirudha
N1 - Funding Information:
Research supported by Core Research Grant (RP03890G), Science and Engineering Research Board (SERB), DST, India
Publisher Copyright:
© 2023, Tusi Mathematical Research Group (TMRG).
PY - 2023/7
Y1 - 2023/7
N2 - 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.
AB - 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.
KW - Compact operators
KW - Discrete modulation spaces
KW - Fourier multipliers
KW - Localization operators
KW - Paracommutators
KW - Paraproducts
KW - Schatten–von Neumann class
KW - Short-time Fourier transform
UR - http://www.scopus.com/inward/record.url?scp=85164325918&partnerID=8YFLogxK
U2 - 10.1007/s43037-023-00286-x
DO - 10.1007/s43037-023-00286-x
M3 - Article
AN - SCOPUS:85164325918
SN - 2662-2033
VL - 17
JO - Banach Journal of Mathematical Analysis
JF - Banach Journal of Mathematical Analysis
IS - 3
M1 - 59
ER -