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Carleman Approximation on Riemannian Manifolds by Harmonic Functions with Newtonian Singularities

Received: 5 October 2014     Accepted: 28 December 2014     Published: 14 January 2015
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Abstract

In 1927, it was proved by Carleman that the real line was a set of Carleman approximation by entire functions. In this paper, the analogous problem for harmonic approximation on Riemannian manifolds is discussed.

Published in American Journal of Applied Mathematics (Volume 3, Issue 1)
DOI 10.11648/j.ajam.20150301.11
Page(s) 1-3
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Harmonic Functions, Harmonic Approximation, Newtonian Functions, Carleman Approximation, Riemannian Manifolds

References
[1] T. Bagby and P. Blanchet, Uniform harmonic approximation on Riemannian manifolds, Journal d’AnalyseMathématique62 (1994), 47-76.
[2] P.M. Gauthier, Carleman approximation on unbounded sets by harmonic functions with Newtonian singularities, in Proceedings of the 8th Conference on analytic functions, Blazejewko, Poland, August, 1982.
[3] T. Carleman, Sur un théorème de Weierstrass, Arkiv för Matematik, Astronomi och Fysik, Band 20B. N:0 4 (1927), 1-5.
[4] T. Bagby and P.M. Gauthier, Approximation by harmonic functions on closed subsets of Riemann surfaces, Journal d’AnalyseMathématique51 (1988), 259-284.
[5] P.M. Gauthier, Uniform approximation, in Complex Potential Theory, Université de Montréal (P.M. Gauthier Editor), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994, 235-271.
[6] T. Bagby and P.M. Gauthier, Harmonic approximation on closed subsets of Riemannian manifolds, in Complex Potential Theory,Université de Montréal (P.M. Gauthier Editor), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994, 75-87.
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  • APA Style

    Pierre Blanchet. (2015). Carleman Approximation on Riemannian Manifolds by Harmonic Functions with Newtonian Singularities. American Journal of Applied Mathematics, 3(1), 1-3. https://doi.org/10.11648/j.ajam.20150301.11

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    ACS Style

    Pierre Blanchet. Carleman Approximation on Riemannian Manifolds by Harmonic Functions with Newtonian Singularities. Am. J. Appl. Math. 2015, 3(1), 1-3. doi: 10.11648/j.ajam.20150301.11

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    AMA Style

    Pierre Blanchet. Carleman Approximation on Riemannian Manifolds by Harmonic Functions with Newtonian Singularities. Am J Appl Math. 2015;3(1):1-3. doi: 10.11648/j.ajam.20150301.11

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  • @article{10.11648/j.ajam.20150301.11,
      author = {Pierre Blanchet},
      title = {Carleman Approximation on Riemannian Manifolds by Harmonic Functions with Newtonian Singularities},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {1},
      pages = {1-3},
      doi = {10.11648/j.ajam.20150301.11},
      url = {https://doi.org/10.11648/j.ajam.20150301.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150301.11},
      abstract = {In 1927, it was proved by Carleman that the real line was a set of Carleman approximation by entire functions. In this paper, the analogous problem for harmonic approximation on Riemannian manifolds is discussed.},
     year = {2015}
    }
    

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Author Information
  • Centre de recherches mathématiques, Université de Montréal, Montréal, Canada

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