English

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

Functional Analysis 2024-03-19 v2

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.

Keywords

Cite

@article{arxiv.2310.10040,
  title  = {The Extended Paley-Wiener Theorem over the Hardy-Sobolev Spaces},
  author = {Detian Liu and Haichou Li and Kit Ian Kou},
  journal= {arXiv preprint arXiv:2310.10040},
  year   = {2024}
}