Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-07-29T16:01:34.958Z Has data issue: false hasContentIssue false
  • English
  • Français

Subharmonic Extensions and Approximations

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier
P. M. Gauthier*
Affiliation:
Département de mathématiques et de statistique et Centre de recherches mathématiques Université de Montréal, CP 6I28-A Montréal, Québec H3C 3J7 e-mail:gauthier@ ere.umontreal.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we extend subharmonic functions defined on closed sets.

Keywords

31B0531C12subharmonic extensions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 1 , 01 March 1994 , pp. 46 - 53
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Anandam, V., Théorie du potentiel dans un espace harmonique sans potentiel positif, Mathématiques, Bull. Sect. Sci. 3(1981), 7–36.Google Scholar
2. Anandam, V., Subharmonic functions outside a compact set in Rn, Proc. Amer. Math. Soc. 84(1982), 52–54.Google Scholar
3. Anandam, V., Superharmonic extensions and the flux, Bull. Sci. Math. 106(1982), 85–92.Google Scholar
4. Armitage, D. H., On the extension of superharmonic functions, J. London Math. Soc. (2) 4(1971), 215–230.Google Scholar
5. Aronsjajn, N., A unique continuation theorem for solutions of elliptic equations or inequalities of second order, J. Math. Pure Appl. 36(1957), 235–249.Google Scholar
6. Bagby, T. and Blanchet, P., Uniform harmonic approximation on Riemannian manifolds, J. d'Analyse Math., to appear.Google Scholar
7. Bauer, H., Harmonische Rdume und ihre Potentialtheorie, SLN 22, Springer-Verlag, Heidelberg, 1966.Google Scholar
8. Bensouda, Ch., Thèse, Université de Montréal, en rédaction.Google Scholar
9. Bliedtner, J. and Hansen, W., Simplicial cones in potential theory, Invent. Math. 29(1975), 83–110.Google Scholar
10. Bliedtner, J. and Hansen, W., Simplicial cones in potential theory II, Invent. Math. 46(1978), 255–275.Google Scholar
11. Brelot, M., Lectures on Potential Theory, Tata Institute, Bombay, 1960.Google Scholar
12. Chen, H. and Gauthier, P. M., A maximum principle for subharmonic and plurisubharmonic functions, Canad. Math. Bull 35(1992), 1–6.Google Scholar
13. Debiard, A. and Gaveau, B., Potentiel fin et algèbres de fonctions analytiques I, J. Funct. Anal. 16(1974), 289–304.Google Scholar
14. Fornaess, J. E. and Wiegerinck, J., Approximation of plurisubharmonic functions, Ark. Mat. 27(1989), 257–272.Google Scholar
15. P. M. Fornaess, J. E. and Wiegerinck, J. Gauthier, Approximation by (pluri)subharmonicfunctions : fusion and localization, Canad. J. Math. 44(1992), 941–950.Google Scholar
16. Gauthier, P. M., Goldstein, M. and Ow, W. H., Uniform approximation on closed sets by harmonie functions with Newtonian singularities, J. London Math. Soc. (2) 28(1983), 71–82.Google Scholar
17. Gauthier, P. M. and Ladouceur, S., Uniform approximation and fine potential theory, J. Approx. Theory 72(1993), 138–140.Google Scholar
18. Guessous, H., Prolongement surharmonique dans un espace harmonique, Notion du flux. Potential Theory, Copenhagen 1979, SLN 787, 121-143, Springer-Verlag, Heidelberg, 1980.Google Scholar
19. de, A. la Pradelle, Approximation et caractère de quasi-analyticité dans la théorie axiomatique des fonctions harmoniques, Ann. Inst. Fourier 17(1967), 383–399.Google Scholar
20. Lax, P., A stability theorem for abstract differential equations and its application to the study of the local behavior of solutions of elliptic equations, Commun. Pure Appl. Math. 9(1956), 747–766.Google Scholar
21. Miranda, C., Partial Differential Equations of Elliptic Type, 2nd. éd., Springer-Verlag, Heidelberg, 1970.Google Scholar
22. Narasimhan, R., Analysis on Real and Complex Manifolds, North-Holland, Amsterdam, 1968.Google Scholar
23. Paramonov, P. V., On harmonic approximation in theC1 -norm, Mat. Sb. 181(1990), 1341–1365; English transi, in Math. USSR Sbornik 71(1992), 183–207.Google Scholar
24. Premalatha, M., On a superharmonic extension, Rev. Roum. Math. Pures Appl. 26( 1981 ), 631–640.Google Scholar
25. Sario, L., Nakai, M., Wang, C. and Chung, L. O., Classification Theory of Riemannian Manifolds, SLN 605, Springer-Verlag, Heidelberg, 1977.Google Scholar
26. Shirinbekov, M., On Hartogs compacts of holomorphy, Mat. Sb. 115( 1981 ), 453-462; English transi, in Math. USSR Sbornik 43(1982), 403–411.Google Scholar
27. Shirinbekov, M., Private communication, 1990.Google Scholar
28. Walsh, J. L., The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions, Bull. Amer. Math. Soc. 35(1929), 499–544.Google Scholar