The Extended Paley-Wiener Theorem over the Hardy-Sobolev Spaces

2023/10/16 by Liu, Detian, Li, Haichou, Kou, Kit Ian
#30A99 #46C07(Primary) #47G10(Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2310.10040

Abstract

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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