Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-plane
Keywords:
continuous wavelet transform, function spaces, Toeplitz type operators, Schatten-Von Neumann class, Besov spacesAbstract
In this paper we consider the decomposition of functions on the upper half-plane into orthogonal subspaces which are isometric to \(L^{2}(\mathbb{R})\) by continuous wavelet transforms. A necessary and sufficient condition for such a decomposition is given. From such a decomposition by general Laguerre polynomials, we define a series of Toeplitz type operators and study the Schatten-Von Neumann classes of these operators.
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