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Distribution of roots of quasianalytic functions

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Abstract

For functions of certain quasianalytic classes C{mn} on (−∞, ∞) we determine a function ξ (x), depending on {mn}, which is such that a sequence {xk} is a sequence of the roots off(x) ε C{mn} if and only if for somea

$$\int_a^\infty {\tfrac{{dn(x)}}{{\xi (x - a}}< \infty ,} $$

where n(x) is a distribution function of the sequence {xk}.

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Literature cited

  1. S. Mandelbrojt, Séries Adherentes, Regularasation des Suites, Applications, Gauthier-Villars, Paris (1952)

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  2. I. I. Hirschman, “On the distributions of the zeros of functions belonging to certain quasianalytic classes,” Amer. J. Math.,72, No. 2, 83–91 (1950).

    Google Scholar 

  3. S. E. Warschawski, “On the conformai mapping of infinite strips,” Trans. Amer. Math. Soc.,51, 280–355 (1942).

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  4. S. P. Geisberg and V. S. Konyukhovskii, “On primary ideals in the ring of functions integrable with a weight,” Uchen. Zap. Tartuskogo Univ., Trudy po Matem, i Mekhan.,9, No. 253, 134–144 (1970).

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  5. S. P. Geisberg, “Asymptotic behavior of quasianalytic functions,” Dokl. Akad. Nauk SSSR,94, No. 5, 999–1000 (1970).

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Authors
  1. V. S. Konyukhovskii
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Additional information

Translated from Matematicheskie Zametki, Vol. 16, No. 1, pp. 3–14, July, 1974.

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Konyukhovskii, V.S. Distribution of roots of quasianalytic functions. Mathematical Notes of the Academy of Sciences of the USSR 16, 585–591 (1974). https://doi.org/10.1007/BF01098808

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  • DOI: https://doi.org/10.1007/BF01098808

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