Buczolich, Zoltán and Seuret, S. (2018) Multifractal properties of typical convex functions. MONATSHEFTE FUR MATHEMATIK, 187 (1). pp. 59-78. ISSN 0026-9255
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Abstract
We study the singularity (multifractal) spectrum of continuous convex functions defined on (Formula presented.). Let (Formula presented.) be the set of points at which f has a pointwise exponent equal to h. We first obtain general upper bounds for the Hausdorff dimension of these sets (Formula presented.), for all convex functions f and all (Formula presented.). We prove that for typical/generic (in the sense of Baire) continuous convex functions (Formula presented.), one has (Formula presented.) for all (Formula presented.) and in addition, we obtain that the set (Formula presented.) is empty if (Formula presented.). Also, when f is typical, the boundary of (Formula presented.) belongs to (Formula presented.). © 2017 Springer-Verlag GmbH Austria, part of Springer Nature
| Item Type: | Article |
|---|---|
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 27 Feb 2023 15:34 |
| Last Modified: | 27 Feb 2023 15:34 |
| URI: | http://real.mtak.hu/id/eprint/160826 |
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