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Rodin, Vladimir Aleksandrovich

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Total publications: 26
Scientific articles: 25

Number of views:
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Abstract pages:6067
Full texts:2448
References:509
Professor
Doctor of physico-mathematical sciences (1993)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 01.01.1947
E-mail: ,
Website: http://www.rodin-va.narod.ru
Keywords: strong summability of the simple and multiple Fourier series in the trigonometric system and Price system; BMO-property of the partial sums; Hardy, Bellman and Cesaro transforms in Fourier analysis; Rademacher and Fourier series in symmetric spaces; multiplication operator on the Rademacher series; the fractal condition in town-planning.

Subject:

BMO-property of the sequence of partial sums of the Fourier series of an summable function is proved. This property has allowed to prove a conjecture of V. Totik about $L_M$ ($M(u)=\exp|u|-1$) — strong summability of the Fourier series almost everywhere. The description of points in which summation is received occurs. The uniform scheme of the proof for trigonometric series and for series in system of characters of various zero-dimensional groups is received. Researches finish a cycle of works of many mathematicians (Hardy, Littlewood, Marcinkiewicz, Totik, Schipp, Gabisoniya, Oskolkov, Gogoladse etc.). As has shown Karaguliyan these investigation in the certain sense is final. For multiple Fourier series it is proved p-strong summability of Fourier series of the function from appropriate Orliczclass. It is established the tensor BMO-property (TBMO) and it is shown, that actually BMO-property in multiple case is absent. The general assertion, relating the phenomenon of rectangular oscillation of the sequence of rectangular partial sums of a multiple Fourier series and the strong summability of that series, is established. A number of papers (with E. M. Semenov) were devoted to studying of the Rademacher series in symmetric spaces. Together with G. Kurbera (Spain) the behaviour of the operator of multiplication to the Rademacher series in symmetric spaces is investigated. In a class of symmetric spaces the exact bounds of shift of spaces BMO, Marcinkiewicz and Orlicz spaces located "close" to the space $L_\infty$ under action on a trigonometrical series of the Hardy operator, Bellman and Chezaro operator are received. With E. V. Rodina the new phenomenon in changes of the megacities connected to town-planning transformations (on an example of areas of Tokyo) is established. The phenomenon connected with the "fractal dimension of Tokyo's streets" is revealed.

Biography

Graduated from Faculty of Mathematics and Mechanics of Voronezh State University (VSU) in 1969 (department of theory of function and geometry). Ph.D. thesis was defended in 1973. D.Sci. thesis was in 1993. A list of my works contains more than 133 titles. Since 2001 I and I. Y. Novikov have led the research seminar at VSU on Fourier analysis and Wavelets theory.

I worked in 1997 at university of city of Budapest under the invitation of the professor F. Schipp, in 2000 at university of city of Seville under the invitation of the professor G. Curbera.

   
Main publications:
  • Rodin V. A., Semenov E. M. Rademacher series in symmetric spaces // Analysis Math. V. 1, no. 3. 1975. P. 207–222.
  • Rodin V. A. The BMO-property of the partial sums of a Fourier series // American Math. Soc. Soviet Math. Dokl. V. 44, no. 1. 1992. P. 294–296.
  • Rodin V. A. Shift of Spaces by Means of the Hardy and Bellman Transforms // American Math. Soc. Functional Analysis and Its Applications, V. 34, no. 2. 2000. P. 151–152.
  • Rodin V. A., Rodina E. V. The fractal dimension of Tokyo"s streets // FRACTALS, V. 8, no. 4. 2000. P. 413–418.
  • Curbera G. P., Rodin V. A. Multiplication operator on the Rademacher series in the Orlicz spaces which are "close to $L_\infty$" // Mathematical Proceedings of the Cambridge Philosophical Society. 2002 (to appear).

http://www.mathnet.ru/eng/person17483
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/261163

Publications in Math-Net.Ru
2021
1. V. A. Rodin, S. V. Sinegubov, “Generalized Kelly strategy”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 14:2 (2021),  100–107  mathnet
2020
2. A. V. Kalach, V. A. Rodin, S. V. Sinegubov, “Optimizing fire-fighting water supply systems using spatial metrics”, J. Comp. Eng. Math., 7:4 (2020),  3–16  mathnet
2019
3. V. A. Rodin, S. V. Sinegubov, “Stochastic modeling of surfaces with modified Gauss functions”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 172 (2019),  96–103  mathnet  elib
4. V. A. Rodin, S. V. Sinegubov, “On reliability of large-scale nets constructed from identical elements”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, 5,  56–62  mathnet; Russian Math. (Iz. VUZ), 63:5 (2019), 51–56  isi
5. V. A. Rodin, S. V. Sinegubov, “Mathematical terrain modelling with the help of modified Gaussian functions”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:3 (2019),  63–73  mathnet  elib
2005
6. V. N. Dumachev, V. A. Rodin, “Evolution of antagonistic-cooperating populations on base of two-parametrical Ferhjust–Pirls model”, Matem. Mod., 17:7 (2005),  11–22  mathnet  mathscinet  zmath
2002
7. G. P. Curbera, V. A. Rodin, “Multipliers on the Set of Rademacher Series in Symmetric Spaces”, Funktsional. Anal. i Prilozhen., 36:3 (2002),  87–90  mathnet  mathscinet  zmath; Funct. Anal. Appl., 36:3 (2002), 244–246  isi  scopus
2000
8. V. A. Rodin, “Shift of Spaces by Means of the Hardy and Bellman Transforms”, Funktsional. Anal. i Prilozhen., 34:2 (2000),  89–91  mathnet  mathscinet  zmath; Funct. Anal. Appl., 34:2 (2000), 154–155  isi
9. S. K. Gorlov, I. Ya. Novikov, V. A. Rodin, “Correction of Haar polynomials used in the compression of graphical information”, Izv. Vyssh. Uchebn. Zaved. Mat., 2000, 7,  6–10  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 44:7 (2000), 4–8
1999
10. V. A. Rodin, “Hardy and Bellman transformations in spaces close to $L_\infty$ and to $L_1$”, Zap. Nauchn. Sem. POMI, 262 (1999),  204–213  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 110:5 (2002), 3016–3021
1998
11. V. A. Rodin, “Strong means and oscillation of multiple Fourier series in multiplicative systems”, Mat. Zametki, 63:4 (1998),  607–616  mathnet  mathscinet  zmath  elib; Math. Notes, 63:4 (1998), 533–541  isi
1994
12. V. A. Rodin, “Strong means and the oscillation of multiple Fourier–Walsh series”, Mat. Zametki, 56:3 (1994),  102–117  mathnet  mathscinet  zmath; Math. Notes, 56:3 (1994), 948–959  isi
1993
13. V. A. Rodin, “Extensions of a Certain Weak Type Operator”, Funktsional. Anal. i Prilozhen., 27:1 (1993),  83–86  mathnet  mathscinet  zmath; Funct. Anal. Appl., 27:1 (1993), 70–73  isi
14. V. A. Rodin, “The tensor BMO-property of the sequence of partial sums of a multiple Fourier series”, Mat. Sb., 184:10 (1993),  91–106  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 80:1 (1995), 211–224  isi
1992
15. V. A. Rodin, “Rectangular oscillation of the sequence of partial sums of a multiple Fourier series and absence of the BMO property”, Mat. Zametki, 52:2 (1992),  152–154  mathnet  mathscinet  zmath; Math. Notes, 52:2 (1992), 863–865  isi
16. A. S. Belov, V. A. Rodin, “Norms of lacunary polynomials in functional spaces”, Mat. Zametki, 51:3 (1992),  137–139  mathnet  mathscinet  zmath; Math. Notes, 51:3 (1992), 318–320  isi
1991
17. V. A. Rodin, “The BMO-property of partial sums of a Fourier series”, Dokl. Akad. Nauk SSSR, 319:5 (1991),  1079–1081  mathnet  mathscinet  zmath; Dokl. Math., 44:1 (1992), 294–296
18. V. A. Rodin, “Pointwise strong summability of multiple Fourier series”, Mat. Zametki, 50:1 (1991),  148–150  mathnet  mathscinet  zmath; Math. Notes, 50:1 (1991), 762–764  isi
19. V. A. Rodin, “The space BMO and strong means of Fourier–Walsh series”, Mat. Sb., 182:10 (1991),  1463–1478  mathnet  mathscinet  zmath; Math. USSR-Sb., 74:1 (1993), 203–218  isi
1989
20. V. A. Rodin, “BMO-strong means of Fourier series”, Funktsional. Anal. i Prilozhen., 23:2 (1989),  73–74  mathnet  mathscinet  zmath; Funct. Anal. Appl., 23:2 (1989), 145–147  isi
1988
21. I. Ya. Novikov, V. A. Rodin, “Characterization of points of $p$-strong summability of trigonometric series, $p\geq 2$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1988, 9,  58–62  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 32:9 (1988), 86–91
1982
22. V. I. Ovchinnikov, V. D. Raspopova, V. A. Rodin, “Sharp estimates of the Fourier coefficients of summable functions and $K$-functionals”, Mat. Zametki, 32:3 (1982),  295–302  mathnet  mathscinet  zmath; Math. Notes, 32:3 (1982), 627–631  isi
1979
23. V. A. Rodin, E. M. Semenov, “Complementability of the subspace generated by the Rademacher system in a symmetric space”, Funktsional. Anal. i Prilozhen., 13:2 (1979),  91–92  mathnet  mathscinet  zmath; Funct. Anal. Appl., 13:2 (1979), 150–151
24. V. A. Rodin, “Membership of the sum of a cosine series with monotone coefficients in a symmetric space”, Izv. Vyssh. Uchebn. Zaved. Mat., 1979, 8,  60–64  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 3:8 (1979), 61–65
1977
25. A. B. Gulisashvili, V. A. Rodin, E. M. Semenov, “Fourier coefficients of summable functions”, Mat. Sb. (N.S.), 102(144):3 (1977),  362–371  mathnet  mathscinet  zmath; Math. USSR-Sb., 31:3 (1977), 319–328  isi
1976
26. V. A. Rodin, “The Hardy-Littlewood theorem for the cosine series in a symmetric space”, Mat. Zametki, 20:2 (1976),  241–246  mathnet  mathscinet  zmath; Math. Notes, 20:2 (1976), 693–696

2012
27. A. O. Vatulyan, V. A. Kabel'kov, T. N. Kabel'kova, S. B. Klimentov, A. I. Kondratenko, A. G. Kusraev, A. N. Nikiforov, A. È. Pasenchuk, V. A. Rodin, V. G. Safronenko, S. M. Sitnik, A. N. Tkachev, V. G. Fetisov, “Aleksandr Nikolaevich Kabel'kov (1947–2011)”, Vladikavkaz. Mat. Zh., 14:2 (2012),  74–77  mathnet

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