Persons
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
 
Trigub, Roald Mikhailovich
Statistics Math-Net.Ru
Total publications: 41
Scientific articles: 40
Presentations: 7

Number of views:
This page:8903
Abstract pages:18741
Full texts:7865
References:1653
Professor
Doctor of physico-mathematical sciences
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail:
Keywords: Fourier multipliers, Fourier series and integrals, comparison of linear operators, approximation of functions with different restrictions, trigonometric Taylor polynomial, best approximation, modulus of smoothness, two-sided approximation estimates, piecewise one-sided approximation, factorization of differential operators.
UDC: 517.5, 517.51, 517.52

Subject:

Fourier Analysis and Approximation of functions.
   
Main publications:
  1. R. M. Trigub, “On the best approximation of non integer constants by polynomials with integer coefficients”, J. Math. Sci., 274, No 3 (2023), 402-421
  2. R. Trigub, “NORMS OF LINEAR FUNCTIONALS, SUMMABILITY OF TRIGONOMETRIC FOURIER SERIES AND WIENER ALGEBRAS Operator Theory and Harmonic Analysis.”, 1 New General Trends and Advances of the Theory, 2021, 549-568 Springer Proceedings in Mathematics & Statistics
  3. E. Liflyand, R. Trigub, “Wiener Algebras and Trigonometric Series in a Coordinated Fashion”, Constructive Approximation, 54 (2021), 185–206
  4. E. Liflyand, R. Trigub, “Conditions for the absolute convergence of Fourier integrals”, J. Appr. Theory, 163:4 (2011), 438–459
  5. R.M. Trigub, E.S. Belinsky, Fourier Analysis and Approximation of Functions, Kluwer- Springer, 2004, 586 pp.

https://www.mathnet.ru/eng/person8511
List of publications on Google Scholar
https://zbmath.org/authors/ai:trigub.roald-m

Publications in Math-Net.Ru Citations
2022
1. R. M. Trigub, “Rogosinsky–Bernstein Polynomial Method of Summation of Trigonometric Fourier Series”, Mat. Zametki, 111:4 (2022),  592–605  mathnet; Math. Notes, 111:4 (2022), 604–615  scopus 1
2021
2. R. M. Trigub, “On Fourier Series on the Torus and Fourier Transforms”, Mat. Zametki, 110:5 (2021),  766–772  mathnet  elib; Math. Notes, 110:5 (2021), 767–772  isi  scopus
2020
3. R. M. Trigub, “Asymptotics of approximation of continuous periodic functions by linear means of their Fourier series”, Izv. RAN. Ser. Mat., 84:3 (2020),  185–202  mathnet  mathscinet  elib; Izv. Math., 84:3 (2020), 608–624  isi  scopus 4
2019
4. R. M. Trigub, “Chebyshev Polynomials and Integer Coefficients”, Mat. Zametki, 105:2 (2019),  302–312  mathnet  mathscinet  elib; Math. Notes, 105:2 (2019), 291–300  isi  scopus 3
2018
5. R. M. Trigub, “The Fourier transform of bivariate functions that depend only on the maximum of the absolute values of their variables”, Mat. Sb., 209:5 (2018),  166–186  mathnet  mathscinet  elib; Sb. Math., 209:5 (2018), 759–779  isi  scopus 1
6. R. M. Trigub, “Letter to the Editors”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:4 (2018),  296  mathnet
2017
7. R. M. Trigub, “On multiply monotone functions.”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:3 (2017),  257–271  mathnet  elib
2016
8. R. M. Trigub, “Almost Everywhere Summability of Fourier Series with Indication of the Set of Convergence”, Mat. Zametki, 100:1 (2016),  163–179  mathnet  mathscinet  elib; Math. Notes, 100:1 (2016), 139–153  isi  scopus 14
2015
9. R. M. Trigub, “Summability of trigonometric Fourier series at $d$-points and a generalization of the Abel–Poisson method”, Izv. RAN. Ser. Mat., 79:4 (2015),  205–224  mathnet  mathscinet  zmath  elib; Izv. Math., 79:4 (2015), 838–858  isi  scopus 15
2014
10. R. M. Trigub, “Generalization of the Abel–Poisson Method for Summations of Fourier Trigonometric Series”, Mat. Zametki, 96:3 (2014),  473–475  mathnet  mathscinet  zmath  elib; Math. Notes, 96:3 (2014), 454–457  isi  scopus 9
2013
11. R. M. Trigub, “The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials”, Mat. Sb., 204:12 (2013),  127–146  mathnet  mathscinet  zmath  elib; Sb. Math., 204:12 (2013), 1819–1838  isi  scopus 9
2010
12. E. R. Liflyand, R. M. Trigub, “On the representation of a function as an absolutely convergent Fourier integral”, Trudy Mat. Inst. Steklova, 269 (2010),  153–166  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 269 (2010), 146–159  isi  scopus 5
2009
13. R. M. Trigub, “Pointwise approximation of periodic functions by trigonometric polynomials with Hermitian interpolation”, Izv. RAN. Ser. Mat., 73:4 (2009),  49–76  mathnet  mathscinet  zmath  elib; Izv. Math., 73:4 (2009), 699–726  isi  elib  scopus 1
2007
14. R. M. Trigub, “Comparison of Linear Differential Operators”, Mat. Zametki, 82:3 (2007),  426–440  mathnet  mathscinet  zmath  elib; Math. Notes, 82:3 (2007), 380–394  isi  scopus 8
2003
15. R. M. Trigub, “Approximation of functions by polynomials with Hermitian interpolation and restrictions on the coefficients”, Izv. RAN. Ser. Mat., 67:1 (2003),  199–221  mathnet  mathscinet  zmath; Izv. Math., 67:1 (2003), 183–206  isi  scopus 4
16. R. M. Trigub, “A Lower Bound for the $L_1$-norm of Fourier Series of Polynomial Type”, Mat. Zametki, 73:6 (2003),  951–953  mathnet  mathscinet  zmath; Math. Notes, 73:6 (2003), 900–903  isi  scopus 4
2002
17. R. M. Trigub, “Compactly supported positive definite radial functions of polynomial kind and maximal smoothness”, Mat. Fiz. Anal. Geom., 9:3 (2002),  394–400  mathnet  mathscinet  zmath 2
18. V. P. Zastavnyi, R. M. Trigub, “Positive-definite splines of special form”, Mat. Sb., 193:12 (2002),  41–68  mathnet  mathscinet  zmath; Sb. Math., 193:12 (2002), 1771–1800  isi  scopus 18
2001
19. R. M. Trigub, “Approximation of Smooth Functions and Constants by Polynomials with Integer and Natural Coefficients”, Mat. Zametki, 70:1 (2001),  123–136  mathnet  mathscinet  zmath  elib; Math. Notes, 70:1 (2001), 110–122  isi 7
1997
20. R. M. Trigub, “A generalization of the Euler–Maclaurin formula”, Mat. Zametki, 61:2 (1997),  312–316  mathnet  mathscinet  zmath; Math. Notes, 61:2 (1997), 253–257  isi 12
21. R. M. Trigub, “Multipliers in the Hardy spaces $H_p(D^m)$ with $p\in (0,1]$ and approximation properties of summability methods for power series”, Mat. Sb., 188:4 (1997),  145–160  mathnet  mathscinet  zmath; Sb. Math., 188:4 (1997), 621–638  isi  scopus 16
1994
22. R. M. Trigub, “Multipliers in the Hardy spaces $H_p(D^m)$ for $p\in(0,1]$ and approximation properties of methods for the summation of power series”, Dokl. Akad. Nauk, 335:6 (1994),  697–699  mathnet  mathscinet  zmath; Dokl. Math., 49:2 (1994), 427–430 4
1993
23. R. M. Trigub, “Direct theorems on approximation of smooth functions by algebraic polynomials on a segment”, Mat. Zametki, 54:6 (1993),  113–121  mathnet  mathscinet  zmath; Math. Notes, 54:6 (1993), 1261–1266  isi 5
1989
24. R. M. Trigub, “Multipliers of Fourier series and approximation of functions by polynomials in the spaces $C$ and $L$”, Dokl. Akad. Nauk SSSR, 306:2 (1989),  292–296  mathnet  mathscinet  zmath; Dokl. Math., 39:3 (1989), 494–498 1
25. R. M. Trigub, “Criterium Based on the Characteristic Function and the Polya-Type Sign for Radial Functions in Several Variables”, Teor. Veroyatnost. i Primenen., 34:4 (1989),  805–810  mathnet  mathscinet  zmath; Theory Probab. Appl., 34:4 (1989), 738–742  isi 12
1987
26. R. M. Trigub, “On the comparison principle for Fourier expansions and existence subspaces in the integral metric”, Trudy Mat. Inst. Steklov., 180 (1987),  219–220  mathnet  zmath; Proc. Steklov Inst. Math., 180 (1989), 259–261
1980
27. O. I. Kuznetsova, R. M. Trigub, “Two-sided estimates of the approximation of functions by Riesz and Marcinkiewicz means”, Dokl. Akad. Nauk SSSR, 251:1 (1980),  34–36  mathnet  mathscinet  zmath 3
28. R. M. Trigub, “Absolute convergence of Fourier integrals, summability of Fourier series, and polynomial approximation of functions on the torus”, Izv. Akad. Nauk SSSR Ser. Mat., 44:6 (1980),  1378–1409  mathnet  mathscinet  zmath; Math. USSR-Izv., 17:3 (1981), 567–593  isi 27
1978
29. R. M. Trigub, “Summability of multiple Fourier series and the approximation of functions on the torus by polynomials”, Dokl. Akad. Nauk SSSR, 240:2 (1978),  276–279  mathnet  mathscinet  zmath 1
1977
30. R. M. Trigub, “The approximation of functions by polynomials with special coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 1977, no. 1,  93–99  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 21:1 (1977), 77–82 3
1976
31. R. M. Trigub, “On integral norms for polynomials”, Mat. Sb. (N.S.), 101(143):3(11) (1976),  315–333  mathnet  mathscinet  zmath; Math. USSR-Sb., 30:3 (1976), 279–295  isi 5
1974
32. R. M. Trigub, “A relation between summability and absolute convergence of Fourier series and transforms”, Dokl. Akad. Nauk SSSR, 217:1 (1974),  34–37  mathnet  mathscinet  zmath 2
33. È. S. Belinskii, R. M. Trigub, “On a relationship in the theory of Fourier series”, Mat. Zametki, 15:5 (1974),  679–682  mathnet  mathscinet  zmath; Math. Notes, 15:5 (1974), 405–407 1
1971
34. R. M. Trigub, “Linear methods of Fourier series summability and the moduli of continuity of various orders”, Sibirsk. Mat. Zh., 12:6 (1971),  1416–1421  mathnet  mathscinet  zmath; Siberian Math. J., 12:6 (1971), 1024–1028 1
1968
35. R. M. Trigub, “Linear summation methods and the absolute convergence of Fourier series”, Izv. Akad. Nauk SSSR Ser. Mat., 32:1 (1968),  24–49  mathnet  mathscinet  zmath; Math. USSR-Izv., 2:1 (1968), 21–46 12
36. R. M. Trigub, “Remarks on Fourier series”, Mat. Zametki, 3:5 (1968),  597–603  mathnet  mathscinet  zmath; Math. Notes, 3:5 (1968), 380–383
1965
37. R. M. Trigub, “The constructive characteristics of certain classes of functions”, Izv. Akad. Nauk SSSR Ser. Mat., 29:3 (1965),  615–630  mathnet  mathscinet  zmath 9
1962
38. R. M. Trigub, “Approximation of functions by polynomials with integer coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 26:2 (1962),  261–280  mathnet  mathscinet  zmath 7
1961
39. R. M. Trigub, “Approximation of functions by polynomials with integral coefficients”, Dokl. Akad. Nauk SSSR, 140:4 (1961),  773–775  mathnet  mathscinet  zmath
1960
40. R. M. Trigub, “Approximation of functions with a given modulus of smoothness on the exterior of a segment and on a half-axis”, Dokl. Akad. Nauk SSSR, 132:2 (1960),  303–306  mathnet  mathscinet  zmath 1
1998
41. V. V. Andrievskii, A. A. Gonchar, V. Ya. Gutlyanskii, V. K. Dzyadyk, A. A. Dovgoshey, N. P. Korneichuk, O. I. Kuznetsova, V. V. Maimeskul, F. G. Maksudov, S. M. Nikol'skii, I. V. Skrypnik, R. M. Trigub, “Vladimir Ivanovich Belyi (obituary)”, Uspekhi Mat. Nauk, 53:6(324) (1998),  231–232  mathnet  mathscinet; Russian Math. Surveys, 53:6 (1998), 1333–1334  isi

Presentations in Math-Net.Ru
1. On the Fourier series and Fourier transforms
R. M. Trigub
International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin
September 10, 2021 10:00   
2. О многочленах Чебышева и целых коэффициентах. О порядке наилучших приближений констант многочленами с целыми и натуральными коэффициентами.
R. M. Trigub
Seminar on Theory of Functions of Real Variables
March 12, 2021 18:30   
3. Связь между алгебрами Винера и рядами Фурье.
R. M. Trigub
Seminar on Theory of Functions of Real Variables
February 12, 2021 18:30   
4. О приближении гладких функций и констант многочленами с целыми и натуральными коэффициентами
R. M. Trigub
Seminar on Theory of Functions of Real Variables
May 12, 2017 18:30
5. О преобразовании Фурье функций нескольких переменных
R. M. Trigub
Seminar on Approximation Theory
May 11, 2017 10:30
6. Приближение функций полиномами
R. M. Trigub
Seminar on Approximation Theory
April 4, 2013 10:30
7. Сравнение линейных дифференциальных операторов
R. M. Trigub
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
April 3, 2013 16:00

Organisations
 
  Contact us:
  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024