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 |
Harmonic Functions, Harmonic Approximation, Newtonian Functions, Carleman Approximation, Riemannian Manifolds
| [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. |
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
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
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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Download@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}
}
TY - JOUR T1 - Carleman Approximation on Riemannian Manifolds by Harmonic Functions with Newtonian Singularities AU - Pierre Blanchet Y1 - 2015/01/14 PY - 2015 N1 - https://doi.org/10.11648/j.ajam.20150301.11 DO - 10.11648/j.ajam.20150301.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 1 EP - 3 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20150301.11 AB - 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. VL - 3 IS - 1 ER -
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