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The Extended Paley-Wiener Theorem over the Hardy-Sobolev Spaces
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We examine how the square-integrable function subspaces are transformed using the holomorphic Fourier transform. On account of this, the extended Paley-Wiener theorem over the Hardy-Sobolev spaces is produced. The theorem also asserts that the reproducing kernel of the Hardy-Sobolev spaces can be found. We discuss the relationship between the disc and the upper half-plane.
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An extension of Haagerup's reduction theorem with applications to subdiagonal subalgebras of general von Neumann algebras
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