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Reconstruction of entire functions from irregularly spaced sample points. (English) Zbl 0860.30029
Let $$G(z)=(z-\lambda_0)\prod^\infty_{n=1} \Biggl(1-{z\over\lambda_n}\Biggr)\Biggl(1-{z\over \lambda_{-n}}\Biggr),$$ where $\lambda_n\in\bbfR$ and $|\lambda_n-n|\le 1/2$, $\forall n\in\bbfZ$. The authors prove that $$\sup_n|G^{(k)}(\lambda_n)/G'(\lambda_n)|<\infty.$$ They apply this result to a problem concerning Hermite interpolation of entire functions of exponential type belonging to $L^p(\bbfR)$. The corresponding problem for functions of several variables is also considered.

30D10Representations of entire functions by series and integrals
30D15Special classes of entire functions; growth estimates
41A05Interpolation (approximations and expansions)
94A05Communication theory
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