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On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net

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Abstract

We obtain a strengthened version of the Hörmander inequality for functions ƒ: ℝ → ℝ, in which, instead of ‖ƒ‖∞, we use the least upper bound of the values of f on a discrete set of points.

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References

  1. J. Hadamard, “Sur le module maximum d'une fonction et de ses dérivées,” C. R. Soc. Math. Frances, 41, 68–72 (1914).

    Google Scholar 

  2. Yu. G. Bossé and G. E. Shilov, “On inequalities between derivatives,” in: Collection of Works of Student Groups of the Moscow State University [in Russian], Moscow University, Moscow (1937) pp. 17–27.

    Google Scholar 

  3. A. Kolmogoroff, “Une généralisation de J. Hadamard entre les bornes superieures des dérivées succèssives d'une fonction,” C. R. Acad. Sci., 207, 764–765 (1938).

    Google Scholar 

  4. A. N. Kolmogorov, “On inequalities between upper bounds of subsequent derivatives of functions on an infinite interval,” Uchen. Zap. Mosk. Univ., Ser. Mat., Issue 30, 3–13 (1939).

    Google Scholar 

  5. L. Hörmander, “New proof and generalization of inequality of Bohr,” Math. Scand., 2, 33–45 (1954).

    MATH  MathSciNet  Google Scholar 

  6. V. N. Konovalov, “A complement to the Kolmogorov inequalities,” Mat. Zametki, 27, Issue 2, 209–215 (1980).

    MATH  MathSciNet  Google Scholar 

  7. T. Bang, “Une inéquality de Kolmogoroff et les fonction presque périodiques,” Det Kgl. Danske Viedenskabemes Selskab. Mathematiskfisiske Meddeleser, 19, No. 4 (1941).

  8. S. Mandelbrojt, Séries Adhérentes. Régularisation des Suites. Applications, Gauthier-Villars, Paris (1952).

    MATH  Google Scholar 

  9. A. A. Ligun, “Inequalities for upper bound of functionals,” Anal. Math., 2, 11–40 (1976).

    Article  MathSciNet  Google Scholar 

  10. N. P. Korneichuk, V. F. Babenko, and A. A. Ligun, Extremal Properties of Polynomials and Splines [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

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Authors
  1. V. F. Babenko
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  2. M. B. Vakarchuk
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Additional information

Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7, pp. 988–992, July, 1997.

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Babenko, V.F., Vakarchuk, M.B. On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net. Ukr Math J 49, 1109–1113 (1997). https://doi.org/10.1007/BF02528756

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  • DOI: https://doi.org/10.1007/BF02528756

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