Journal of Operator Theory

Volume 90, Issue 2, Autumn 2023 pp. 385-400.

Localization operators on the unit disk

Authors: Aparajita Dasgupta (1), Santosh Kumar Nayak (2), M.W. Wong (3)
Author institution: (1) Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India
(2) Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India
(3) Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada

Summary: We show that on the unit disk, the localization operators associated to admissible wavelets and separable symbols are paracommutators. We have obtained conditions on the symbol of the localization operator such that it can be expressed in terms of a paraproduct and also under certain other condition on the symbol it is a Fourier multiplier.

DOI: http://dx.doi.org/10.7900/jot.2021dec20.2350
Keywords: unit disk, square-integrable representations, localization operators, paracommutators, paraproducts, Fourier multipliers

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