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arXiv:2004.00608 [math.FA]AbstractReferencesReviewsResources

On the characterization of constant functions through nonlocal functionals

Massimo Gobbino, Nicola Picenni

Published 2020-04-01Version 1

We provide a counterexample to an open question concerning a characterization of constant functions through double integrals that involve different quotients. This counterexample requires the construction of an unbounded function whose difference quotients avoid a sequence of intervals with endpoints that diverge to infinity.

Comments: 6 pages
Categories: math.FA
Subjects: 26A30, 26A45
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