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We show that every continuous and dually translation invariant valuation on the space of Lipschitz functions on the unit sphere of $\mathbb{R}^n$, $n\ge2$, can be decomposed uniquely into a sum of homogeneous valuations of degree $0$, $1$ and $2$. In
Externí odkaz:
http://arxiv.org/abs/2401.05913
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere $S^{n-1}$. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded with respec
Externí odkaz:
http://arxiv.org/abs/2005.05419
We provide an integral representation for continuous, rotation invariant and dot product invariant valuations defined on the space Lip$(S^{n-1})$ of Lipschitz continuous functions on the unit $n-$sphere.
Comment: 27 pages
Comment: 27 pages
Externí odkaz:
http://arxiv.org/abs/1906.04118
Publikováno v:
In Journal of Functional Analysis 15 February 2021 280(4)
Publikováno v:
In Advances in Mathematics 3 June 2020 366
Publikováno v:
Mathematische Annalen; Oct2023, Vol. 387 Issue 1/2, p321-352, 32p
Akademický článek
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Publikováno v:
E-Prints Complutense. Archivo Institucional de la UCM
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We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere Sn−1. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded with respect t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::a49080d86441c5834cedaba463403473
https://eprints.ucm.es/id/eprint/74378/
https://eprints.ucm.es/id/eprint/74378/
Autor:
Lazzeri, Davide, Pieri, Marco, Lazzeri, Stefano, Colizzi, Livio, Giannotti, Giordano, Pagnini, Daniele, Stabile, Marco, Gatti, Gian Luca, Massei, Alessandro
Publikováno v:
In Burns 2009 35(4):600-605