To the 90th Birthday of Roald Mikhailovich Trigub
DOI:
https://doi.org/10.37069/3154-8229-2026-40-1Keywords:
Roald Mikhailovich Trigub, Fourier analysis, approximation theory, Fourier multipliers, mathematical analysis, Donetsk mathematical school, scientific biographyAbstract
The article is dedicated to the 90th anniversary of the well-known mathematician R.M. Trigub. We briefly outline the main stages of his scientific biography, his contribution to the development of Fourier Analysis and Approximation Theory, as well as his role in the formation of the Donetsk scientific school. His pedagogical and scientific-organizational activities are also highlighted.
References
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Kolomoitsev, Yu.S., & Trigub, R.M. (2013). On the nonclassical approximation method for periodic functions by trigonometric polynomials. Journal of Mathematical Sciences, 188(2), 113–127. https://doi.org/10.1007/s10958-012-1111-x
Kolomoitsev, Yu. S. (2017). On moduli of smoothness and averaged differences of fractional order. Fractional Calculus and Applied Analysis, 20(4), 988–1009. https://doi.org/10.1515/fca-2017-0051
Liflyand, E., Samko, S., & Trigub, R. (2012). The Wiener algebra of absolutely convergent Fourier integrals: An overview. Analysis and Mathematical Physics, 2(1), 1–68. https://doi.org/10.1007/s13324-012-0025-6
Liflyand, E., & Trigub, R. (2011). Conditions for the absolute convergence of Fourier integrals. Journal of Approximation Theory, 163(4), 438–459. https://doi.org/10.1016/j.jat.2010.11.001
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Trigub, R.M. (1962). Approximation of functions by polynomials with integer coefficients. Mathematics of the USSR-Izvestiya, 26(2), 261–280.
Trigub, R.M. (1968). Linear summation methods and the absolute convergence of Fourier series. Mathematics of the USSR-Izvestiya, 2(1), 21–46. https://doi.org/10.1070/IM1968v002n01ABEH000627
Trigub, R.M. (1976). On integral norms for polynomials. Mathematics of the USSR-Sbornik, 30(3), 279–295. https://doi.org/10.1070/SM1976v030n03ABEH002274
Trigub, R.M. (1981). Absolute convergence of Fourier integrals, summability of Fourier series, and approximation of functions by polynomials on the torus. Mathematics of the USSR-Izvestiya, 17(3), 567–593. https://doi.org/10.1070/IM1981v017n03ABEH001372
Trigub, R.M. (1989). Fourier series multipliers and approximation of functions by polynomials in the spaces $C$ and $L$. Soviet Mathematics Doklady, 39, 494–498.
Trigub, R.M. (1989). A criterion for a characteristic function and a Pólya-type theorem for radial functions of several variables. Theory of Probability and Its Applications, 34(4), 805–810.
Trigub, R.M. (1996). Some topics in Fourier analysis and approximation theory. arXiv preprint funct-an/9612008.
Trigub, R.M. (1993). Direct theorems of approximation of smooth functions by algebraic polynomials on a segment. Mathematical Notes, 54(6), 1261–1266. https://doi.org/10.1007/BF01209088
Trigub, R.M. (1997). A generalization of the Euler–Maclaurin formula. Mathematical Notes, 61(2), 312–316. https://doi.org/10.4213/mzm1504
Trigub, R.M. (1997). Multipliers in Hardy spaces $H_p(D^m)$ for $p ∈ (0,1]$ and approximation properties of summation methods for power series. Sbornik: Mathematics, 188(4), 145–160. https://doi.org/10.1070/SM1997v188n04ABEH000221
Trigub, R.M. (2001). Approximation of smooth functions and constants by polynomials with integer and natural coefficients. Mathematical Notes, 70(1), 110–122. https://doi.org/10.1023/A:1010282120209
Trigub, R.M. (2002). Compactly supported positive definite radial functions of polynomial kind and maximal smoothness. Mathematical Physics, Analysis and Geometry, 9(3), 394–400.
Trigub, R.M. (2003). Approximation of functions by polynomials with Hermite interpolation and restrictions on coefficients. Izvestiya: Mathematics, 67(1), 199–221. https://doi.org/10.1070/IM2003v067n01ABEH000424
Trigub, R.M. (2003). A lower bound for the $L_1$-norm of a Fourier series of power type. Mathematical Notes, 73(6), 951–953. https://doi.org/10.1023/A:1024070318039
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Trigub, R.M. (2005). Fourier multipliers and $K$-functionals in spaces of smooth functions. Ukrainian Mathematical Bulletin, 2(2), 239–284.
Trigub, R.M. (2007). Comparison of linear differential operators. Mathematical Notes, 82(3), 426–440. https://doi.org/10.1134/S0001434607090118
Trigub, R.M. (2007). A note on the paper of S.A. Telyakovskii: “Some properties of Fourier series of functions with bounded variation”. East Journal on Approximations, 13(1), 1–6.
Trigub, R.M. (2008). A generalization of the Riemann–Lebesgue lemma. Ukrainian Mathematical Bulletin, 5(3), 394–405.
Trigub, R.M. (2009). Pointwise approximation of periodic functions by trigonometric polynomials with Hermite interpolation. Izvestiya: Mathematics, 73(4), 49–76. https://doi.org/10.1070/IM2009v073n04ABEH002463
Trigub, R.M. (2009). Approximation of functions by polynomials with various constraints. Journal of Contemporary Mathematical Analysis, 44(4), 230–242. https://doi.org/10.3103/S1068362309040049
Trigub, R.M. (2013). The exact order of approximation of periodic functions by Bernstein-Stechkin polynomials. Sbornik: Mathematics, 204(11–12), 1819–1838. htps://doi.org/10.1070/SM2013v204n12ABEH004362
Trigub, R.M. (2015). Summability of trigonometric Fourier series at $d$-points and a generalization of the Abel–Poisson method. Izvestiya: Mathematics, 79(4), 838–858. https://doi.org/10.4213/im8240
Trigub, R.M. (2016). Almost everywhere summability of Fourier series with indication of the convergence set. Mathematical Notes, 100(1), 139–153. https://doi.org/10.4213/mzm11124
Trigub, R.M. (2021). On Fourier series on the torus and Fourier transforms. Mathematical Notes, 110(5), 767--772. https://doi.org/10.1134/S0001434621110134
Trigub, R.M. (2021). Norms of linear functionals, summability of trigonometric Fourier series and Wiener algebras. In Operator Theory and Harmonic Analysis. OTHA 2020 (pp. 549–568). Springer Proceedings in Mathematics & Statistics (Vol. 357). Springer. https://doi.org/10.1007/978-3-030-77493-6_33
Trigub, R.M. (2022). Rogosinsky–Bernstein polynomial method of summation of trigonometric Fourier series. Mathematical Notes, 111(4), 604–615. https://doi.org/10.1134/S0001434622030294
Trigub, R.M. (2026). On trigonometric Fourier series and Wiener algebras. Journal of Mathematical Sciences, 299(1), 96–119. https://doi.org/10.1007/s10958-026-08399-y
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Zastavnyi, V.P., & Trigub, R.M. (2002). Positive-definite splines of a special form. Sbornik: Mathematics, 193(12), 1771–1800. https://doi.org/10.1070/SM2002v193n12ABEH000699
