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Generalized Double Fourier Sine Series

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The paper is focused on studies of connections between the integrability of a two-variable function near the origin and the behavior of its generalized Fourier sine series. This problem has direct relevance to issues of asymptotic behavior of Fourier series with monotone coefficients in a neighborhood of the origin.

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  1. R. P. Boas, “Integrability of Nonnegative Trigonometric Series,” Tohoku Math. J. Ser. 2 16 (4), 368 (1964).

    Article  MATH  Google Scholar 

  2. M. I. D'yachenko, “Integrability of Functions and Fourier Coefficients,” Vestn. Mosk. Univ. Matem. Mekhan., No. 4, 18 (1977).

    MathSciNet  MATH  Google Scholar 

  3. N. K. Bari, Trigonometric Series (Fizmatgiz, Moscow, 1961) [in Russian].

    Google Scholar 

  4. A. Yu. Popov, “Estimates of the Sums of Sine Series with Monotone Coefficients of Certain Classes,” Matem. Zametki 74 (6), 877 (2003) [Math. Notes 74 (5-6), 829 (2003)].

    Article  MathSciNet  Google Scholar 

  5. S. A. Telyakovskii, “A Problem Suggested by R. Boas,” Matem. Zametki 5 (4), 437 (1969) [Math. Notes 5 (4), 263 (1969)].

    MATH  Google Scholar 

  6. S. A. Telyakovskii, “The Problem of Behavior of Sine Series Near the Origin,” Makedon. Akad. Nauk. Umet. Oddel. Mat.-Tehn. Nauk. Prilozi. 21 (1-2), 47 (2000).

    MathSciNet  Google Scholar 

  7. A. Zh. Ydyrys, “Asymptotics of Multiple Trigonometric Series with Monotone Coefficients,” Vestn. Mosk. Univ. Matem. Mekhan. No. 6, 14 (2015).

    Google Scholar 

  8. K. S. Kazaryan, “Summability and Convergence Almost Everywhere of Generalized Fourier and Fourier-Haar Series,” Izvestiya Akad. Nauk Arm. SSR 20 (2), 145 (1985).

    MathSciNet  MATH  Google Scholar 

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Correspondence to K. A. Oganesyan.

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Original Russian Text © K.A. Oganesyan. 2018. published in Vestnik Moskouskogo Universiteta. Matematika. Mekhanika. 2018. Vol. 73, No. 1, pp. 11-19.

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Oganesyan, K.A. Generalized Double Fourier Sine Series. Moscow Univ. Math. Bull. 73, 9–16 (2018).

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