Uniform approximation of continuous functions on compact sets by biharmonic functions

Mustapha Chadli; Mohamed El Kadiri

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 3, page 427-435
  • ISSN: 0010-2628

Abstract

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We give a characterization of functions that are uniformly approximable on a compact subset K of n by biharmonic functions in neighborhoods of K .

How to cite

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Chadli, Mustapha, and El Kadiri, Mohamed. "Uniform approximation of continuous functions on compact sets by biharmonic functions." Commentationes Mathematicae Universitatis Carolinae 44.3 (2003): 427-435. <http://eudml.org/doc/249180>.

@article{Chadli2003,
abstract = {We give a characterization of functions that are uniformly approximable on a compact subset $K$ of $\mathbb \{R\}^n$ by biharmonic functions in neighborhoods of $K$.},
author = {Chadli, Mustapha, El Kadiri, Mohamed},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {biharmonic function; finely biharmonic function; approximation of continuous functions on compact sets; biharmonic function; finely biharmonic function; approximation of continuous functions on compact sets},
language = {eng},
number = {3},
pages = {427-435},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Uniform approximation of continuous functions on compact sets by biharmonic functions},
url = {http://eudml.org/doc/249180},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Chadli, Mustapha
AU - El Kadiri, Mohamed
TI - Uniform approximation of continuous functions on compact sets by biharmonic functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 3
SP - 427
EP - 435
AB - We give a characterization of functions that are uniformly approximable on a compact subset $K$ of $\mathbb {R}^n$ by biharmonic functions in neighborhoods of $K$.
LA - eng
KW - biharmonic function; finely biharmonic function; approximation of continuous functions on compact sets; biharmonic function; finely biharmonic function; approximation of continuous functions on compact sets
UR - http://eudml.org/doc/249180
ER -

References

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  4. El Kadiri M., Fonctions finement biharmoniques, Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 24 (2000), 43-62. (2000) MR1827006
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  8. Helms L.L., Introduction to Potential Theory, Wiley-Interscience, 1969. Zbl0188.17203MR0261018
  9. Hervé R.M., Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier 12 (1962), 415-517. (1962) MR0139756
  10. Lyons T.J., Cones of lower semicontinuous functions and a characterization of finely hyperharmonic functions, Math. Ann. 261 (1982), 293-297. (1982) MR0679790
  11. Smyrnelis E.P., Axiomatique des fonctions biharmoniques, 1e section, Ann. Inst. Fourier 26.1 (1975), 35-98. (1975) Zbl0295.31006
  12. Smyrnelis E.P., Axiomatique des fonctions biharmoniques, 2e section, Ann. Inst. Fourier 26.3 (1976), 1-47. (1976) MR0477101

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