Abstract
ABSTRACTWe define the windowed Fourier transform, called also the Gabor transform, associated with singular partial differential operators. We establish Plancherel theorem, orthogonality property and inversion formula for this transform. Next, we define the localization operators , called also Gabor multipliers, associated with two windows and with symbol σ. First, we study the boundedness and compactness of the operators . Last, we define the Schatten-von Neumann class and we prove that the localization operators belong to .
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