Riesz capacities of a set due to Dobiński

Nicola Arcozzi; Nikolaos Chalmoukis

doi:10.5802/crmath.332

Analyse harmonique, Combinatoire

Riesz capacities of a set due to Dobiński

Nicola Arcozzi ¹ ; Nikolaos Chalmoukis ¹

¹ Dipartimento di Matematica, Università di Bologna, 40126, Bologna, Italy

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 679-685.

Résumé

We study the Riesz $(a, p)$ -capacity of the so called Dobiński set. We characterize the values of the parameters $a$ and $p$ for which the $(a, p)$ -Riesz capacity of the Dobiński set is positive. In particular we show that the Dobiński set has positive logarithmic capacity, thus answering a question of Dayan, Fernandéz and González. We approach the problem by considering the dyadic analogues of the Riesz $(a, p)$ -capacities which seem to be better adapted to the problem.

Reçu le : 2021-11-11
Révisé le : 2022-01-14
Accepté le : 2022-01-18
Publié le : 2022-06-22

Zbl

DOI : 10.5802/crmath.332

Classification : 31C20, 30C85, 31A15, 11J83
Mots clés : Riesz capacity, Logarithmic capacity, Dobiński set, Dyadic capacity, Non-linear capacity, Diophantine approxmation

Affiliations des auteurs :

Nicola Arcozzi ¹ ; Nikolaos Chalmoukis ¹

¹ Dipartimento di Matematica, Università di Bologna, 40126, Bologna, Italy

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Riesz capacities of a set due to {Dobi\'nski}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {679--685},
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     year = {2022},
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     language = {en},
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Nicola Arcozzi; Nikolaos Chalmoukis. Riesz capacities of a set due to Dobiński. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 679-685. doi : 10.5802/crmath.332. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.332/

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