REAL

Upper Minkowski dimension estimates for convex restrictions

Buczolich, Zoltán (2017) Upper Minkowski dimension estimates for convex restrictions. ACTA MATHEMATICA HUNGARICA, 152 (1). pp. 84-108. ISSN 0236-5294

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Abstract

We show that there are functions f in the Holder class , such that is neither convex nor concave for any with . Our earlier result shows that for the typical/generic , there is always a set such that is convex and . The analogous statement for monotone restrictions is the following: there are functions in the Holder class , such that is not monotone on with . This statement is not true for the range of parameters and the main theorem of this paper for the parameter range cannot be obtained by integration of the result about monotone restrictions.

Item Type: Article
Uncontrolled Keywords: RESTRICTION; Convexity; MINKOWSKI DIMENSION; Hölder class; Hölder class;
Subjects: Q Science / természettudomány > Q1 Science (General) / természettudomány általában
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 23 May 2023 09:05
Last Modified: 23 May 2023 09:05
URI: http://real.mtak.hu/id/eprint/165829

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