| Title:
|
Characterization of functions whose forward differences are exponential polynomials (English) |
| Author:
|
Almira, J. M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
435-442 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given $\{h_1,\cdots,h_{t}\}$ a finite subset of $\mathbb{R}^d$, we study the continuous complex valued functions and the Schwartz complex valued distributions $f$ defined on $\mathbb{R}^d$ with the property that the forward differences $\Delta_{h_k}^{m_k}f$ are (in distributional sense) continuous exponential polynomials for some natural numbers $m_1,\cdots,m_t$. (English) |
| Keyword:
|
functional equations |
| Keyword:
|
exponential polynomials |
| Keyword:
|
generalized functions |
| Keyword:
|
forward differences |
| MSC:
|
39A70 |
| MSC:
|
39B52 |
| idZBL:
|
Zbl 06837077 |
| idMR:
|
MR3737116 |
| DOI:
|
10.14712/1213-7243.2015.224 |
| . |
| Date available:
|
2017-12-12T06:43:59Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146988 |
| . |
| Reference:
|
[1] Aksoy A., Almira J.M.: On Montel and Montel-Popoviciu theorems in several variables.Aequationes Math. 89 (2015), no. 5, 1335–1357. Zbl 1337.47051, MR 3390165, 10.1007/s00010-014-0329-8 |
| Reference:
|
[2] Almira J.M.: Montel's theorem and subspaces of distributions which are $\Delta^m$-invariant.Numer. Funct. Anal. Optim. 35 (4) (2014), 389–403. Zbl 1327.47005, MR 3177061, 10.1080/01630563.2013.813537 |
| Reference:
|
[3] Almira J.M., Abu-Helaiel K.F.: On Montel's theorem in several variables.Carpathian J. Math. 31 (2015), 1–10. Zbl 1349.47007, MR 3408590 |
| Reference:
|
[4] Almira J.M., Székelyhidi L.: Local polynomials and the Montel theorem.Aequationes Math. 89 (2015), 329-338. Zbl 1321.43007, MR 3340213, 10.1007/s00010-014-0308-0 |
| Reference:
|
[5] Almira J.M., Székelyhidi L.: Montel–type theorems for exponential polynomials.Demonstr. Math. 49 (2016), no. 2, 197–212. Zbl 1344.43002, MR 3507933 |
| Reference:
|
[6] Anselone P.M., Korevaar J.: Translation invariant subspaces of finite dimension.Proc. Amer. Math. Soc. 15 (1964), 747–752. Zbl 0138.37903, MR 0169048, 10.1090/S0002-9939-1964-0169048-7 |
| Reference:
|
[7] Hardy G.H., Wright E.M.: An Introduction to the Theory of Numbers. Fifth edition.The Clarendon Press, Oxford University Press, New York, 1979. MR 0568909 |
| Reference:
|
[8] Waldschmidt M.: Topologie des Points Rationnels.Cours de Troisi\`{e}me Cycle 1994/95 Université P. et M. Curie (Paris VI), 1995. |
| . |
