| Title:
|
Sets of determination for parabolic functions on a half-space (English) |
| Author:
|
Ranošová, Jarmila |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
497-513 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize all subsets $M$ of $\Bbb R^n \times \Bbb R^+$ such that $$ \sup\limits_{X\in \Bbb R^n \times \Bbb R^+}u(X) = \sup\limits_{X\in M}u(X) $$ for every bounded parabolic function $u$ on $\Bbb R^n \times \Bbb R^+$. The closely related problem of representing functions as sums of Weierstrass kernels corresponding to points of $M$ is also considered. The results provide a parabolic counterpart to results for classical harmonic functions in a ball, see References. As a by-product the question of representability of probability continuous distributions as sums of multiples of normal distributions is investigated. (English) |
| Keyword:
|
heat equation |
| Keyword:
|
parabolic function |
| Keyword:
|
Weierstrass kernel |
| Keyword:
|
set of determination |
| Keyword:
|
decomposition of $L_1(\Bbb R^n)$ |
| Keyword:
|
normal distribution |
| MSC:
|
31B10 |
| MSC:
|
35C15 |
| MSC:
|
35K05 |
| MSC:
|
35K15 |
| MSC:
|
60E99 |
| idZBL:
|
Zbl 0808.35043 |
| idMR:
|
MR1307276 |
| . |
| Date available:
|
2009-01-08T18:12:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118689 |
| . |
| Reference:
|
[1] Aikawa H.: Sets of determination for harmonic function in an NTA domains.preprint, 1992. MR 1376083 |
| Reference:
|
[2] Bonsall F.F.: Decomposition of functions as sums of elementary functions.Quart J. Math. Oxford (2) 37 (1986), 129-136. MR 0841422 |
| Reference:
|
[3] Bonsall F.F.: Domination of the supremum of a bounded harmonic function by its supremum over a countable subset.Proc. Edinburgh Math. Soc. 30 (1987), 441-477. Zbl 0658.31001, MR 0908454 |
| Reference:
|
[4] Bonsall F.F.: Some dual aspects of the Poisson kernel.Proc. Edinburgh Math. Soc. 33 (1990), 207-232. Zbl 0704.31001, MR 1057750 |
| Reference:
|
[5] Doob J.L.: Classical Potential Theory and Its Probabilistic Counterpart.Springer-Verlag New York (1984). Zbl 0549.31001, MR 0731258 |
| Reference:
|
[6] Gardiner S.J.: Sets of determination for harmonic function.Trans. Amer. Math. Soc. 338 (1993), 233-243. MR 1100694 |
| Reference:
|
[7] Rudin W.: Functional Analysis.McGraw-Hill Book Company (1973). Zbl 0253.46001, MR 0365062 |
| Reference:
|
[8] Dudley Ward N.F.: Atomic Decompositions of Integrable or Continuous Functions.D.Phil Thesis, University of York, 1991. |
| . |
