Characterization of functions whose forward differences are exponential polynomials

J. M. Almira

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 4, page 435-442
  • ISSN: 0010-2628

Abstract

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Given { h 1 , ⋯ , h t } a finite subset of ℝ d , we study the continuous complex valued functions and the Schwartz complex valued distributions f defined on ℝ d with the property that the forward differences Δ h k m k f are (in distributional sense) continuous exponential polynomials for some natural numbers m 1 , ⋯ , m t .

How to cite

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Almira, J. M.. "Characterization of functions whose forward differences are exponential polynomials." Commentationes Mathematicae Universitatis Carolinae 58.4 (2017): 435-442. <http://eudml.org/doc/294704>.

@article{Almira2017,
abstract = {Given $\lbrace h_1,\cdots ,h_\{t\}\rbrace $ 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 $m_1,\cdots ,m_t$.},
author = {Almira, J. M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {functional equations; exponential polynomials; generalized functions; forward differences},
language = {eng},
number = {4},
pages = {435-442},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Characterization of functions whose forward differences are exponential polynomials},
url = {http://eudml.org/doc/294704},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Almira, J. M.
TI - Characterization of functions whose forward differences are exponential polynomials
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 4
SP - 435
EP - 442
AB - Given $\lbrace h_1,\cdots ,h_{t}\rbrace $ 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 $m_1,\cdots ,m_t$.
LA - eng
KW - functional equations; exponential polynomials; generalized functions; forward differences
UR - http://eudml.org/doc/294704
ER -

References

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  1. Aksoy A., Almira J.M., 10.1007/s00010-014-0329-8, Aequationes Math. 89 (2015), no. 5, 1335–1357. Zbl1337.47051MR3390165DOI10.1007/s00010-014-0329-8
  2. Almira J.M., 10.1080/01630563.2013.813537, Numer. Funct. Anal. Optim. 35 (4) (2014), 389–403. Zbl1327.47005MR3177061DOI10.1080/01630563.2013.813537
  3. Almira J.M., Abu-Helaiel K.F., On Montel's theorem in several variables, Carpathian J. Math. 31 (2015), 1–10. Zbl1349.47007MR3408590
  4. Almira J.M., Székelyhidi L., 10.1007/s00010-014-0308-0, Aequationes Math. 89 (2015), 329-338. Zbl1321.43007MR3340213DOI10.1007/s00010-014-0308-0
  5. Almira J.M., Székelyhidi L., Montel–type theorems for exponential polynomials, Demonstr. Math. 49 (2016), no. 2, 197–212. Zbl1344.43002MR3507933
  6. Anselone P.M., Korevaar J., 10.1090/S0002-9939-1964-0169048-7, Proc. Amer. Math. Soc. 15 (1964), 747–752. Zbl0138.37903MR0169048DOI10.1090/S0002-9939-1964-0169048-7
  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. MR0568909
  8. Waldschmidt M., Topologie des Points Rationnels, Cours de Troisième Cycle 1994/95 Université P. et M. Curie (Paris VI), 1995. 

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