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On approximation properties of one trigonometric system

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Abstract

We obtain the criteria of completeness and minimality of a system. We also obtain an analog of the Paley-Wiener theorem related to this system.

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References

  1. Wiener, N. and Paley, R. Fourier Transforms in the Complex Domain (Amer. Math. Soc., 1934; Nauka, Moscow, 1964).

    MATH  Google Scholar 

  2. Vinnits’kii, B. V. and Shavala, O. V. “The Boundedness of Solutions of a Second-Order Linear Differential Equation, and a Boundary Value Equation for the Bessel Equation” (Ukrainian), Mat. Stud. 30, No. 1, 31–41 (2008).

    MathSciNet  Google Scholar 

  3. Lutsenko, V. I. and Yulmukhametov, R. S. “Generalization of the Paley-Wiener Theorem on Weighted Spaces,” Math. Notes 48, No. 5–6, 1131–1136 (1991).

    MathSciNet  Google Scholar 

  4. Tuan, V. K. and Zayed, A. I. “Paley-Wiener Type Theorems for a Class of Integral Transform,” J.Math. Anal. Appl. 226, No. 1, 200–226 (2002).

    Article  MathSciNet  Google Scholar 

  5. Khabibullin, B. N. Completeness of Systems of Exponents and Sets of Uniqueness (RITs BashGU, Ufa, 2008) [in Russian].

    Google Scholar 

  6. Laine, I. Nevanlinna Theory and Complex Differential Equations (Walter de Gruiter, Berlin, 1993).

    Book  Google Scholar 

  7. Sedletskii, A. M. Classes of Analytic Fourier Transformations (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  8. Levin, B. Lectures on Entire Functions (AMS, Providence, RI, 1996).

    MATH  Google Scholar 

  9. Vynnyts’kyi, B. V. and Khats’, R.V. “Some Approximation Properties of the Systems of Bessel Functions of Index −3/2,” Mat. Stud. 34, No. 2, 152–159 (2010).

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Drohobych State Pedagogical University, ul. Stryiska 3, Drohobych, Lviv region, 82100, Ukraine

    B. V. Vinnitskii & V. N. Dilnyi

Authors
  1. B. V. Vinnitskii
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  2. V. N. Dilnyi
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Correspondence to V. N. Dilnyi.

Additional information

Original Russian Text © B.V. Vinnitskii, V.N. Dilnyi, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 11, pp. 13–25.

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Vinnitskii, B.V., Dilnyi, V.N. On approximation properties of one trigonometric system. Russ Math. 58, 10–21 (2014). https://doi.org/10.3103/S1066369X14110024

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  • DOI: https://doi.org/10.3103/S1066369X14110024

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