Abstract
We obtain sufficient conditions for the basis property of the family of exponentials
in the Sobolev spaceH s(0,a) in terms of the behavior of the generating function, which is an entire function of exponential type with zeros λ n . This result is a generalization of the Levin-Golovin theorem on the basis property of the family of exponentials generated by a function of sine type inL 2(0,a). We apply the theorem obtained to the interpolation of entire functions of exponential type; this application is a generalization of the Kotel’nikov-Shannon theorem in signal theory.
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Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 163–172, August, 2000.
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Avdonin, S.A., Ivanov, S.A. The Levin-Golovin theorem for sobolev spaces. Math Notes 68, 145–153 (2000). https://doi.org/10.1007/BF02675339
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DOI: https://doi.org/10.1007/BF02675339