Two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian groups associated to right-H-translation invariant functions

By using a coset of closed subgroup, we define a generalization of directionally sensitive variant Fourier like transform for locally compact abelian (LCA) topological groups. Further we have showed that this transform have some resembles with short time Fourier transform (STFT). For particular choices of LCA group and its closed subgroup, this operator gives directional STFT of function with respect to some windows. That means the present theory extends the theory of directional STFT in LCA groups. We study the interesting properties of two wavelet multipliers on locally compact abelian topological groups associated to this transform, known as generalized two wavelet multipliers, and show that these operators are L p -bounded for 1 ≤ p ≤ ∞, and are in Schatten-von Neumann classes, S p . For S 1 class we obtain their traces, and finally determine the connection between generalized two wavelet multipliers and generalized Landau-Pollak-Slepian operators. Mathematics Subject Classification (2010). Primary 47G10, 47G30, Secondary 42C40.