Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.01948 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917651902627840 |
|---|---|
| author | Maslouhi, Mostafa Okoudjou, Kasso A. |
| author_facet | Maslouhi, Mostafa Okoudjou, Kasso A. |
| contents | The HRT conjecture states that any finite collection of time-frequency shifts of a non-zero square-integrable function on the real line is linearly independent. In this paper, we establish the linear independence of finite systems of time-frequency shifts of a non-zero meromorphic function. Consequently, we prove that the conjecture is true for any square-integrable function on $\mathbb{R}$ that can be extended to an analytic function on $\mathbb{C}$ except on finitely many points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01948 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The HRT conjecture for a class of meromorphic functions Maslouhi, Mostafa Okoudjou, Kasso A. Complex Variables Primary 42C15 Secondary 42C40 The HRT conjecture states that any finite collection of time-frequency shifts of a non-zero square-integrable function on the real line is linearly independent. In this paper, we establish the linear independence of finite systems of time-frequency shifts of a non-zero meromorphic function. Consequently, we prove that the conjecture is true for any square-integrable function on $\mathbb{R}$ that can be extended to an analytic function on $\mathbb{C}$ except on finitely many points. |
| title | The HRT conjecture for a class of meromorphic functions |
| topic | Complex Variables Primary 42C15 Secondary 42C40 |
| url | https://arxiv.org/abs/2303.01948 |