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Conditions of Convergence Almost Everywhere for the Convolution of a Function with Delta-Shaped Kernel to this Function

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Ukrainian Mathematical Journal Aims and scope

We establish sufficient conditions for the convergence of the convolution of a function with delta-shaped kernel to this function. These conditions are used for the construction of the subspaces of solutions of differential equations and systems of these equations isometric to the spaces of real functions.

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References

  1. D. M. Bushev, “Isometry of functional spaces with different number of variables,” Ukr. Mat. Zh., 50, No. 8, 1027–1045 (1998); English translation: Ukr. Math. J., 50, No. 8, 1170–1191 (1998).

  2. I. P. Natanson, Theory of Functions of Real Variable [in Russian], Nauka, Moscow (1974).

  3. E. M. Stein and G.Weiss, Introduction to Fourier Analysis of Euclidean Spaces [Russian translation], Princeton Univ. Press, Princeton, NJ (1971).

  4. A. I. Stepanets, Rate of Convergence of Fourier Series on the Classes of Convolutions [in Russian], Preprint No. 96.11, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1996).

  5. N. P. Korneichuk, Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).

  6. A. N. Kolmogorov and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1972).

  7. V. A. Il’in and É. G. Poznyak, Foundations of Mathematical Analysis. Part II [in Russian], Nauka, Moscow (1980).

  8. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Their Applications [in Russian], Nauka i Tekhnika, Minsk (1987).

  9. N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965).

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

  11. R. E. Edwards, Fourier Series. A Modern Introduction, Vol. 1, Springer, New York (1979).

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 11, pp. 1461–1476, November, 2015.

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Bushev, D.M., Kharkevych, Y.I. Conditions of Convergence Almost Everywhere for the Convolution of a Function with Delta-Shaped Kernel to this Function. Ukr Math J 67, 1643–1661 (2016). https://doi.org/10.1007/s11253-016-1180-y

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  • DOI: https://doi.org/10.1007/s11253-016-1180-y

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