On zeros of some entire functions

Hryniv, Rostyslav; Mykytyuk, Yaroslav

doi:10.1090/S0002-9947-08-04714-4

On zeros of some entire functions

Authors: Rostyslav O. Hryniv and Yaroslav V. Mykytyuk
Journal: Trans. Amer. Math. Soc. 361 (2009), 2207-2223
MSC (2000): Primary 30D15; Secondary 42A38
DOI: https://doi.org/10.1090/S0002-9947-08-04714-4
Published electronically: November 17, 2008
MathSciNet review: 2465834
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Abstract: We study the distribution of zeros for entire functions of the form $\sin z + \int_{0}^1 f(t)\mathrm{e}^{iz(1-2t)}\,dt$ with belonging to a space $X \hookrightarrow L_1(0,1)$ . For a large class $\mathscr{X}$ of spaces (including, e.g., the spaces for all $p\in[1,\infty]$ ) we show that $z_k=\pi k + \zeta_k$ , where $(\zeta_k)_{k\in\mathbb{Z}}$ is the sequence of Fourier coefficients for some function in , and study properties of the induced mapping $g\mapsto f$ .

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