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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Andersen, Nils Byrial 2015. Real Paley–Wiener theorems and Roe's theorem associated with the Opdam–Cherednik transform. Journal of Mathematical Analysis and Applications, Vol. 427, Issue. 1, p. 47.

    Andersen, Nils Byrial 2015. Roe's theorem revisited. Integral Transforms and Special Functions, Vol. 26, Issue. 3, p. 165.

    Chung, Soon-Yeong and Chung, Yun-Sung 2014. Tempered Gevrey distributions with spectral gaps and their applications. Integral Transforms and Special Functions, Vol. 25, Issue. 2, p. 85.

    2014. Correspondence Between Geometric and Differential Definitions of the Sine and Cosine. The College Mathematics Journal, Vol. 45, Issue. 1, p. 11.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 141, Issue 3
  • November 2006, pp. 509-519

Generalization of characterizations of the trigonometric functions

  • DOI:
  • Published online: 01 December 2006

Suppose that $P(D)$ is a linear differential operator with complex coefficients and $\{f_k\}_{k \in \mathbb{Z}}$ is a two-sided sequence of complex-valued functions on $\mathbb{R}$ such that $f_{k+1} \,{=}\, P(D)f_k$ with the following growth condition: there exist $a\,{\in}\,[0,1)$ and $N\,{\geq}\,0$ such that $|f_k(x)|\,{\leq}\,M_{|k|}\exp (N|x|^a)$, where the sequence $\{M_k\}_{k=0}^{\infty}$ satisfies that for any $\varepsilon\,{>}\,0$, the sequence $\{{M_k}/{(1+\varepsilon)^{k}}\}_{k=0}^{\infty}$ has a bounded subsequence. Then $f_0$ is an entire function of an exponential growth. This result is a generalization of those of Roe, Burkill and Howard.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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