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Conditions for positive definiteness of restrictions of entire functions of exponential type to Rn

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References

  1. M. Plancherel and G. Polya, “Fonctions entiéres et intégrales de Fourier multiples,” Comm. Math. Helv.,10, 110–163 (1937–38).

    MathSciNet  Google Scholar 

  2. M. L. Cartwright, “On certain integral functions of order one,” Quart. Journal of Math. Oxf. Ser.,7, 46–55 (1936).

    MATH  Google Scholar 

  3. R. P. Boas, “Entire functions bounded on a line,” Duke Math. Journal,6, 46–55 (1940).

    Google Scholar 

  4. B. Ya. Levin, “On functions of finite degree that are bounded on sequences of points,” Dokl. Akad. Nauk SSSR,65, No. 3, 265–268 (1949).

    MATH  Google Scholar 

  5. V. N. Logvinenko, “On one multidimensional generalization of a theorem of Cartwright,” Dokl. Akad. Nauk SSSR,219, No. 3, 546–549 (1974).

    MATH  MathSciNet  Google Scholar 

  6. V. N. Logvinenko, “Conditions for boundedness and conditions for slow growth on the real hyperplane for entire functions of exponential type,” Sib. Math. J.,29, No. 4, 126–138 (1988).

    MATH  MathSciNet  Google Scholar 

  7. N. I. Akhiezer, Lectures on Integral Transforms. X [in Russian] (1984).

  8. S. Mandel'broit, Quasianalytic Classes of Functions [in Russian], Moscow-Leningrad (1937).

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Authors
  1. V. N. Logvinenko
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Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 56, pp. 88–94, 1991.

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Logvinenko, V.N. Conditions for positive definiteness of restrictions of entire functions of exponential type to Rn . J Math Sci 76, 2512–2516 (1995). https://doi.org/10.1007/BF02364908

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  • DOI: https://doi.org/10.1007/BF02364908

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