Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.20240 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912382848073728 |
|---|---|
| author | Charpentier, Stéphane Maronikolakis, Konstantinos |
| author_facet | Charpentier, Stéphane Maronikolakis, Konstantinos |
| contents | Let $(τ_n)_n$ be a sequence of real numbers in $(1,+\infty)$. Using potential theoretic methods, we prove quantitative results - Bernstein-Walsh type theorems - about uniform approximation by polynomials of the form $\sum_{k=\lfloor \frac{n}{τ_n} \rfloor}^na_k z^k$, on the union of two disjoint compact sets, one containing 0 and the other not. Moreover, we reveal the interplay between the compact sets and the asymptotic behaviour of the sequence $(τ_n)_n$. As applications of our results, we prove the existence of frequently universal Taylor series, with respect to the natural and the logarithmic densities, providing solutions to two problems posed by Mouze and Munnier. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative incomplete polynomial approximation and frequently universal Taylor series Charpentier, Stéphane Maronikolakis, Konstantinos Complex Variables 30K15, 41A10, 47A16, 30E10, 41A25 Let $(τ_n)_n$ be a sequence of real numbers in $(1,+\infty)$. Using potential theoretic methods, we prove quantitative results - Bernstein-Walsh type theorems - about uniform approximation by polynomials of the form $\sum_{k=\lfloor \frac{n}{τ_n} \rfloor}^na_k z^k$, on the union of two disjoint compact sets, one containing 0 and the other not. Moreover, we reveal the interplay between the compact sets and the asymptotic behaviour of the sequence $(τ_n)_n$. As applications of our results, we prove the existence of frequently universal Taylor series, with respect to the natural and the logarithmic densities, providing solutions to two problems posed by Mouze and Munnier. |
| title | Quantitative incomplete polynomial approximation and frequently universal Taylor series |
| topic | Complex Variables 30K15, 41A10, 47A16, 30E10, 41A25 |
| url | https://arxiv.org/abs/2504.20240 |