Sharp Schoenberg type inequalities and the de Bruin--Sharma problem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914181240848384 |
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| author | Tang, Quanyu Zhang, Teng |
| author_facet | Tang, Quanyu Zhang, Teng |
| contents | In this paper, we confirm two conjectures proposed by Georgiev, Gómez-Serrano, Tao, and Wagner~\cite{GGTW25} on Schoenberg type inequalities of order $4$, thereby providing a complete solution to the de Bruin--Sharma problem. We further develop a new interpolation framework to study Schoenberg type inequalities and, in particular, give a new proof of Pereira's result. Motivated by Sendov's conjecture, we then derive sharp Schoenberg type inequalities of orders $-1$ and $-2m$ (with $m \in \mathbb{N}$), as well as non-sharp inequalities valid for all negative orders $p \le -1$. Finally, we discuss a dual counterpart of the Schoenberg type inequalities of order $-2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Schoenberg type inequalities and the de Bruin--Sharma problem Tang, Quanyu Zhang, Teng Complex Variables Functional Analysis 30C10, 47A57, 15A42 In this paper, we confirm two conjectures proposed by Georgiev, Gómez-Serrano, Tao, and Wagner~\cite{GGTW25} on Schoenberg type inequalities of order $4$, thereby providing a complete solution to the de Bruin--Sharma problem. We further develop a new interpolation framework to study Schoenberg type inequalities and, in particular, give a new proof of Pereira's result. Motivated by Sendov's conjecture, we then derive sharp Schoenberg type inequalities of orders $-1$ and $-2m$ (with $m \in \mathbb{N}$), as well as non-sharp inequalities valid for all negative orders $p \le -1$. Finally, we discuss a dual counterpart of the Schoenberg type inequalities of order $-2$. |
| title | Sharp Schoenberg type inequalities and the de Bruin--Sharma problem |
| topic | Complex Variables Functional Analysis 30C10, 47A57, 15A42 |
| url | https://arxiv.org/abs/2508.10341 |