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Reconstruction of entire functions from irregularly spaced sample points. (English) Zbl 0860.30029

Let

G(z)=(z-λ 0 ) n=1 1 - z λ n 1 - z λ -n ,

where λ n and |λ n -n|1/2, n. The authors prove that

sup n |G (k) (λ n )/G ' (λ n )|<·

They apply this result to a problem concerning Hermite interpolation of entire functions of exponential type belonging to L p (). The corresponding problem for functions of several variables is also considered.

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