| Title:
|
Pointwise and locally uniform convergence of holomorphic and harmonic functions (English) |
| Author:
|
Štěpničková, Libuše |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
665-678 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces. (English) |
| Keyword:
|
Osgood's theorem |
| Keyword:
|
approximation |
| Keyword:
|
maximum principle |
| Keyword:
|
harmonic space |
| Keyword:
|
elliptic PDE's |
| MSC:
|
30E10 |
| MSC:
|
31B05 |
| MSC:
|
31D05 |
| MSC:
|
35J15 |
| MSC:
|
35J99 |
| idZBL:
|
Zbl 1009.31002 |
| idMR:
|
MR1756543 |
| . |
| Date available:
|
2009-01-08T18:56:29Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119122 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[GGG] Gardiner S.J., Goldstein M., GowriSankaran K.: Global approximation in harmonic spaces.Proc. Amer. Math. Soc. 122 (1994), 213-221. Zbl 0809.31006, MR 1203986 |
| Reference:
|
[He] Hervé R.M.: Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel.Ann. Inst. Fourier 12 (1962), 415-571. MR 0139756 |
| Reference:
|
[HR] Hartogs F., Rosenthal A.: Über Folgen analytischer Funktionen.Math. Ann. 100 (1928), 212-263. MR 1512483 |
| Reference:
|
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| Reference:
|
[Pra] Pradelle A.: Approximation et caractère de quasi-analyticit dans la thorie axiomatique des fonctions harmoniques.Ann. Inst. Fourier 17 (1967), 383-399. MR 0227456 |
| Reference:
|
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| Reference:
|
[U1] Ullrich P.: Punktweise und lokal gleichmäßige Konvergenz von Folgen holomorpher Funktionen I..Math. Semesterber. 41 (1994), 69-75. Zbl 0815.30002, MR 1332472 |
| Reference:
|
[U2] Ullrich P.: Punktweise und lokal gleichmäßige Konvergenz von Folgen holomorpher Funktionen II..Math. Semesterber. 41 (1994), 81-87. Zbl 0815.30003, MR 1332472 |
| . |
