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Interpolation by Generalized Exponential Series

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Abstract

We prove an analogue of one of Cesàro’s results and use it to study the problem of interpolation by generalized exponential series, namely, by series whose terms themselves are Dirichlet series.

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References

  1. V. V. Napalkov and K. Zimens, “De la Vallée Poussin problem in the kernel of the convolution operator on the half-plane,” Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki 19 (2), 283–292 (2015).

    Article  Google Scholar 

  2. V. V. Napalkov, “Complex analysis and the Cauchy problem for convolution operators,” Proc. Steklov Inst. Math. 235, 158–161 (2001).

    MathSciNet  MATH  Google Scholar 

  3. V. V. Napalkov and A. A. Nuyatov, “The multipoint de la Vallée-Poussin problem for a convolution operator,” Sb. Math. 203 (2), 224–233 (2012).

    Article  MathSciNet  Google Scholar 

  4. K. R. Zabirova and V. V. Napalkov, “The Dunkl convolution operators and multipoint de la Vallée–Poussin problem,” Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki 1(30), 70–81 (2013).

    Article  Google Scholar 

  5. V. V. Napalkov and A. U. Mullabaeva, “On one class of differential operators and their application,” Proc. Steklov Inst. Math. (Suppl.) 288 (Suppl. 1), 142–155 (2015).

    Article  Google Scholar 

  6. V. V. Napalkov and A. U. Mullabaeva, “The multiple interpolation de La Vallée Poussin problem,” Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki 19 (1), 63–77 (2015).

    Article  Google Scholar 

  7. S. G. Merzlyakov and S. V. Popenov, “Interpolation with multiplicity by series of exponentials in \(H(\mathbb C)\) with nodes on the real axis,” Ufa Math. J. 5 (3), 127–140 (2013).

    Article  MathSciNet  Google Scholar 

  8. S. G. Merzlyakov, “Interpolation and absolutely convergent series in Fréchet spaces,” Sb. Math. 210 (1), 105–144 (2019).

    Article  MathSciNet  Google Scholar 

  9. G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis 1. Band: Reihen, Integralrechnung, Funktionentheorie (Springer- Verlag, Berlin–New York, 1964).

    Book  Google Scholar 

  10. M. Eidelheit, “Zur Theorie der Systeme linearer Gleichungen,” Studia Math. 6, 139–148 (1936).

    Article  Google Scholar 

  11. A. F. Leont’ev, Exponential Series (Nauka, Moscow, 1976) [in Russian].

    MATH  Google Scholar 

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Authors and Affiliations

  1. Ufa Federal Research Center of Russian Academy of Science, 450008, Ufa, Russia

    S. G. Merzlyakov

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  1. S. G. Merzlyakov
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Correspondence to S. G. Merzlyakov.

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Merzlyakov, S.G. Interpolation by Generalized Exponential Series. Math Notes 109, 94–101 (2021). https://doi.org/10.1134/S0001434621010119

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  • DOI: https://doi.org/10.1134/S0001434621010119

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