Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.03718 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916148949286912 |
|---|---|
| author | Chatziafratis, Andreas Hatziafratis, Telemachos |
| author_facet | Chatziafratis, Andreas Hatziafratis, Telemachos |
| contents | In this note, we prove that the Fourier-Laplace transform of the typical function (i.e., generic in the sense of Baire category theorem) in the Schwartz class of the half-line, being analytic in the lower half of the complex plane, has natural boundary the axis of the real numbers. We also provide variations and generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density in the half-line Schwartz space of functions whose Fourier-Laplace transform has natural boundary the real line Chatziafratis, Andreas Hatziafratis, Telemachos Complex Variables Mathematical Physics Functional Analysis General Topology In this note, we prove that the Fourier-Laplace transform of the typical function (i.e., generic in the sense of Baire category theorem) in the Schwartz class of the half-line, being analytic in the lower half of the complex plane, has natural boundary the axis of the real numbers. We also provide variations and generalizations. |
| title | Density in the half-line Schwartz space of functions whose Fourier-Laplace transform has natural boundary the real line |
| topic | Complex Variables Mathematical Physics Functional Analysis General Topology |
| url | https://arxiv.org/abs/2403.03718 |