Reply to 'Comments on Graphon Signal Processing' [arXiv:2310.14683]
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914637069418496 |
|---|---|
| author | Ruiz, Luana Chamon, Luiz F. O. Ribeiro, Alejandro |
| author_facet | Ruiz, Luana Chamon, Luiz F. O. Ribeiro, Alejandro |
| contents | This technical note addresses an issue [arXiv:2310.14683] with the proof (but not the statement) of [arXiv:2003.05030, Proposition 4]. The statement of the proposition is correct, but the proof as written in [arXiv:2003.05030] is not and due to a typo in the manuscript, a reference to the correct proof is effectively missing. In the sequel, we present [arXiv:2003.05030, Proposition 4] and its proof. The proof follows from results in [2] that we reproduce here for clarity of exposition.
Since the statement of the proposition remains correct, no change in the results of [arXiv:2003.05030] are required. In particular, Lemma 3 and Lemma 4 showing spectral convergence of graphs to graphons, Theorem 1 showing convergence of the GFT to the WFT, and Theorems 3 and 4 showing convergence of graph to graphon filters, remain valid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reply to 'Comments on Graphon Signal Processing' [arXiv:2310.14683] Ruiz, Luana Chamon, Luiz F. O. Ribeiro, Alejandro Signal Processing This technical note addresses an issue [arXiv:2310.14683] with the proof (but not the statement) of [arXiv:2003.05030, Proposition 4]. The statement of the proposition is correct, but the proof as written in [arXiv:2003.05030] is not and due to a typo in the manuscript, a reference to the correct proof is effectively missing. In the sequel, we present [arXiv:2003.05030, Proposition 4] and its proof. The proof follows from results in [2] that we reproduce here for clarity of exposition. Since the statement of the proposition remains correct, no change in the results of [arXiv:2003.05030] are required. In particular, Lemma 3 and Lemma 4 showing spectral convergence of graphs to graphons, Theorem 1 showing convergence of the GFT to the WFT, and Theorems 3 and 4 showing convergence of graph to graphon filters, remain valid. |
| title | Reply to 'Comments on Graphon Signal Processing' [arXiv:2310.14683] |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2401.05326 |