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Decomposability of continuous functions from Nikol'skii classes into multiple fourier integrals

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Literature cited

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    S. M. Nikol'skii, Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1969).

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    Sh. A. Alimov and V. A. Il'in, “Spectral decompositions corresponding to an arbitrary self-adjoint extension of the Laplacian,” Dokl. Akad. Nauk SSSR,193, No. 1, 9–12 (1970).

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    Sh. A. Alimov, V. A. Il'in, and E. M. Nikishin, “Questions of convergence of multiple trigonometric series and spectral decompositions,” Usp. Mat. Nauk,31, No. 6, 29–83 (1976).

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    Sh. A. Alimov, “Decomposability of continuous functions from the Sobolev classes with respect to eigenfunctions of the Laplacian,” Sibirsk. Mat. Zh.,19, No. 4, 721–734 (1978).

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    N. N. Kozlova, “Riesz summability of continuous functions from Nikol'skii classes,” Differents. Uravnen.,20, No. 1, 46–56 (1984).

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Translated from Matematicheskie Zametki, Vol. 47, No. 2, pp. 3–7, February, 1990.

The author expresses sincere thanks to Professor Sh. A. Alimov for discussions of the results of the paper

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Ashurov, R.R. Decomposability of continuous functions from Nikol'skii classes into multiple fourier integrals. Mathematical Notes of the Academy of Sciences of the USSR 47, 107–110 (1990). https://doi.org/10.1007/BF01156817

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Keywords

  • Fourier
  • Continuous Function
  • Fourier Integral
  • Skii Class
  • Multiple Fourier Integral