| Title:
|
Uniform approximation of continuous functions on compact sets by biharmonic functions (English) |
| Author:
|
Chadli, Mustafa |
| Author:
|
El Kadiri, Mohamed |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
427-435 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a characterization of functions that are uniformly approximable on a compact subset $K$ of $\Bbb R^n$ by biharmonic functions in neighborhoods of $K$. (English) |
| Keyword:
|
biharmonic function |
| Keyword:
|
finely biharmonic function |
| Keyword:
|
approximation of continuous functions on compact sets |
| MSC:
|
31A30 |
| MSC:
|
41A30 |
| MSC:
|
42A10 |
| idZBL:
|
Zbl 1127.31300 |
| idMR:
|
MR2025811 |
| . |
| Date available:
|
2009-01-08T19:30:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119399 |
| . |
| Reference:
|
[1] Constantinescu C., Cornea A.: Potential Theory on Harmonic Spaces.Springer Verlag, Heidelberg, 1972. Zbl 0248.31011, MR 0419799 |
| Reference:
|
[2] Debiard A., Gaveau B.: Potentiel fin et algèbre de fonctions analytiques, I.J. Funct. Anal. 16 (1974), 289-304. MR 0380426 |
| Reference:
|
[3] El Kadiri M.: Représentation intégrale dans le cadre de la théorie axiomatique des fonctions biharmoniques.Rev. Roumaine Math. Pures Appl. 42 (1997), 7-8, 579-589. MR 1650389 |
| Reference:
|
[4] El Kadiri M.: Fonctions finement biharmoniques.Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 24 (2000), 43-62. MR 1827006 |
| Reference:
|
[5] Fuglede B.: Finely harmonic functions.Lecture Notes in Math. 289, Springer, Berlin-Heidelberg-New York, 1972. Zbl 0248.31010, MR 0450590 |
| Reference:
|
[6] Fuglede B.: On the mean value property of finely harmonic and finely hyperharmonic functions.Aequationes Math. 39 (1990), 198-203. Zbl 0709.31002, MR 1045667 |
| Reference:
|
[7] Gauthier P.M., Ladouceur S.: Uniform approximation and fine potential theory.J. Approx. Theory 72.2 (1993), 138-140. Zbl 0782.31002, MR 1204136 |
| Reference:
|
[8] Helms L.L.: Introduction to Potential Theory.Wiley-Interscience, 1969. Zbl 0188.17203, MR 0261018 |
| Reference:
|
[9] Hervé R.M.: Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel.Ann. Inst. Fourier 12 (1962), 415-517. MR 0139756 |
| Reference:
|
[10] Lyons T.J.: Cones of lower semicontinuous functions and a characterization of finely hyperharmonic functions.Math. Ann. 261 (1982), 293-297. MR 0679790 |
| Reference:
|
[11] Smyrnelis E.P.: Axiomatique des fonctions biharmoniques.1e section, Ann. Inst. Fourier 26.1 (1975), 35-98. Zbl 0295.31006 |
| Reference:
|
[12] Smyrnelis E.P.: Axiomatique des fonctions biharmoniques.2e section, Ann. Inst. Fourier 26.3 (1976), 1-47. MR 0477101 |
| . |
