Abstract
In this paper, we define the wavelet multiplier and Landau–Pollak–Slepian (L.P.S) operators on the Hilbert space \(L^2(G)\), where G is a locally compact abelian topological group and investigate some of their properties. In particular, we show that they are bounded linear operators, and are in Schatten p-class spaces, \(1 \le p \le \infty \), and we determine their trace class.
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Abdullah, M.K., Kamyabi Gol, R.A. & Janfada, M. On wavelet multipliers and Landau–Pollak–Slepian operators on locally compact abelian topological groups. J. Pseudo-Differ. Oper. Appl. 10, 257–267 (2019). https://doi.org/10.1007/s11868-019-00286-2
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DOI: https://doi.org/10.1007/s11868-019-00286-2
Keywords
- Locally compact abelian group
- Dual group
- Wavelet multiplier operator
- Landau–Pollak–Slepian operator
- Admissible wavelets
- Unitary representation