Approximation by Solutions of Elliptic Equations and Extension of Subharmonic Functions

Chapter
First Online:
Part of the Fields Institute Communications book series (FIC, volume 81)

Abstract

In this review we present the main results jointly obtained by the authors and André Boivin (1955–2014) during the last 20 years. We also recall some important theorems obtained with colleagues and give new applications of the above mentioned results. Several open problems are also formulated.

Keywords

Elliptic operator Banach space of distributions Approximation on closed sets L-analytic and L-meromorphic functions Localization operator Cm-extension of subharmonic functions 

2010 Mathematics Subject Classification.

Primary 30E10 31A05; Secondary 31A35 31B05 35B60 35J30 
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Notes

Acknowledgements

Paul Gauthier was supported by NSERC (Canada) and Entente France-Québec. Petr V. Paramonov was partially supported by the Programme for the Support of Leading Scientific Schools of the Russian Federation (grant NSh-9110.2016.1).

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Département de Mathématiques et de StatistiqueUniversité de MontréalMontréalCanada
  2. 2.Mechanics and Mathematics FacultyMoscow State (Lomonosov) UniversityMoscowRussia

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