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Inequality of the Turan type for trigonometric polynomials and conjugate trigonometric polynomials in L 0

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Ukrainian Mathematical Journal Aims and scope

We study inequalities of the Turan type for trigonometric polynomials and conjugate trigonometric polynomials in the quasinorm of L 0 and derivatives of any order. We present expressions for constants in these inequalities and obtain double-sided estimates for them.

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References

  1. S. N. Bernstein, Collection of Works [in Russian], Academy of Sciences of the USSR, Moscow (1952–1959).

    Google Scholar 

  2. G. Szegő, “Über einen satz des Herr Serge Bernstein,” Schriftenr. Konigsberg. Gelehrten Ges., 5, No. 4, 59–70 (1928).

    Google Scholar 

  3. A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge (1959).

    MATH  Google Scholar 

  4. V. I. Ivanov, “Direct and inverse theorems of approximation theory in the metric of L p for 0 < p < 1,” Mat. Zametki, 18, 641–658 (1975).

    MathSciNet  MATH  Google Scholar 

  5. É. A. Storozhenko, V. G. Krotov, and P. Oswald, “Direct and inverse theorems of the Jackson type in the spaces L p , 0 < p < 1,” Mat. Sb., 98, No. 3, 395–415 (1975).

    MathSciNet  Google Scholar 

  6. V. V. Arestov, “On integral inequalities for trigonometric polynomials and their derivatives,” Izv. Akad. Nauk SSSR, Ser. Mat., 45, 3–22 (1981).

    MathSciNet  Google Scholar 

  7. V. V. Arestov, “Szegő inequality for a conjugate trigonometric polynomial in L 0 ,” Mat. Zametki, 56, Issue 6, 10–26 (1994).

    MathSciNet  Google Scholar 

  8. P. Turan, “Über die Ableitung von polynomen,” Compos. Math., 7, 89–95 (1939).

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  10. É. A. Storozhenko, “On the Mahler problem of zeros of a polynomial and its derivative,” Mat. Sb., 187, No. 5, 111–120 (1996).

    MathSciNet  Google Scholar 

  11. É. A. Storozhenko, “Inequality of the Turan type for complex-valued polynomials in the L0 -metric,” Izv. Vyssh. Uchebn. Zaved. Ser. Mat., No. 5, 1–6 (2008).

  12. G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer, New York (1972).

    MATH  Google Scholar 

  13. V. V. Arestov, “Integral inequalities for algebraic polynomials on a unit circle,” Mat. Zametki, 48, Issue 4, 7–18 (1990).

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Odessa National University; Institute of Mathematics, Economy, and Mechanics, Odessa, Ukraine

    A. N. Adamov

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  1. A. N. Adamov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 7, pp. 986–994, July, 2009.

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Adamov, A.N. Inequality of the Turan type for trigonometric polynomials and conjugate trigonometric polynomials in L 0 . Ukr Math J 61, 1169–1179 (2009). https://doi.org/10.1007/s11253-009-0263-4

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  • DOI: https://doi.org/10.1007/s11253-009-0263-4

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