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Mat. Zametki, 2004, Volume 76, Issue 6, Pages 874–882 (Mi mz159)  

This article is cited in 1 scientific paper (total in 1 paper)

Sobolev Capacities of Configurations with Multiple Points in Poisson Space

O. V. Pugachev

N. E. Bauman Moscow State Technical University

Abstract: In this work, we study the difference between the space of all configurations and the space of configurations without multiple points, in the sense of topological properties, Poisson measures, and capacities generated by Sobolev functions. We prove that, under certain conditions, the set of configurations having multiple points has zero Sobolev $C_{r,p}$ capacity in the space of configurations on $\mathbb R^d$ with Poisson measure.

DOI: https://doi.org/10.4213/mzm159

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English version:
Mathematical Notes, 2004, 76:6, 816–823

Bibliographic databases:

UDC: 517.98
Received: 07.10.2003

Citation: O. V. Pugachev, “Sobolev Capacities of Configurations with Multiple Points in Poisson Space”, Mat. Zametki, 76:6 (2004), 874–882; Math. Notes, 76:6 (2004), 816–823

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pugachev O.V., “Sobolevskie emkosti v prostranstve neevklidovykh konfiguratsii”, Vestnik moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N.E. Baumana. seriya: estestvennye nauki, 2011, 109–123  elib
  • Математические заметки Mathematical Notes
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