Lie groups,
symmetric spaces,
representations of groups,
function spaces,
approximations of functions,
Bessel transform,
generalize translation of Bessel,
approximation of functions,
Jackson theorems,
entire functions of exponential type,
Bernstein inequality,
Nikol'skii spaces,
Besov spaces.
Harmonic analysis on Lie groups and homogeneous spaces; function spaces and approximations of functions on homogeneous manifolds; special functions and its applications.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1977 (department of differential geometry). Ph.D. thesis was defended in 1984. D.Sci. thesis was defended in 2001. A list of my works contains more than 100 titles.
Main publications:
S. S. Platonov. Garmonicheskii analiz Besselya i priblizhenie funktsii na polupryamoi. Izv. RAN. Ser. matem., 2007, 71:5, 149–196.
S. S. Platonov. Preobrazovanie Fure funktsii, udovletvoryayuschikh usloviyu Lipshitsa, na simmetricheskikh prostranstvakh ranga 1. Sib. matem. zhurn., 2005, 46:6, 1375–1388.
S. S. Platonov. Invariantnye podprostranstva v nekotorykh funktsionalnykh prostranstvakh na simmetricheskikh prostranstvakh. III.
Izv. RAN. Ser. matem., 2002, 66:1, 167–202.
S. S. Platonov. Teoremy dzheksonovskogo tipa na kompaktnykh simmetricheskikh prostranstvakh ranga 1. Sib. matem. zhurn., 2001, 42:1, 136–148.
S. S. Platonov. Ob odnom podkhode k teorii prostranstv tipa Nikolskogo–Besova na odnorodnykh mnogoobraziyakh.
Fundament. i prikl. matem., 2000, 6:1, 207–223.
S. S. Platonov. Ob ekvivalentnykh normirovkakh prostranstv $H_p^r$ na kompaktnykh odnorodnykh mnogoobraziyakh.
Matem. zametki, 2000, 68:6, 898–909.
S. S. Platonov. Invariantnye podprostranstva v nekotorykh funktsionalnykh prostranstvakh na simmetricheskikh prostranstvakh. II.
Izv. RAN. Ser. matem., 1998, 62:2, 131–168.
S. S. Platonov. Priblizheniya na kompaktnykh simmetricheskikh prostranstvakh ranga 1.
Matem. sb., 1997, 188:5, 113–130.
S. S. Platonov. Invariantnye podprostranstva v nekotorykh funktsionalnykh prostranstvakh na simmetricheskikh prostranstvakh. I. Izv. RAN. Ser. matem., 1995, 59:5, 127–172.
S. S. Platonov. Podprostranstva, invariantnye otnositelno obobschennykh sdvigov. Matem. zametki, 1990, 47:6, 91–101.
S. S. Platonov. Invariantnye podprostranstva v nekotorykh funktsionalnykh prostranstvakh na $n$-mernom prostranstve Lobachevskogo.
Matem. sb., 1988, 137(179):4(12), 435–461.
S. S. Platonov, “On the Fourier–Walsh Transform of Functions from Dyadic Dini–Lipschitz Classes on the Semiaxis”, Mat. Zametki, 108:2 (2020), 236–251; Math. Notes, 108:2 (2020), 229–242
S. S. Platonov, “Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces”, Izv. RAN. Ser. Mat., 82:1 (2018), 198–224; Izv. Math., 82:1 (2018), 186–211
4.
S. S. Platonov, “An Analog of Titchmarsh's Theorem for the Fourier–Walsh Transform”, Mat. Zametki, 103:1 (2018), 101–110; Math. Notes, 103:1 (2018), 96–103
S. S. Platonov, “On spectral synthesis in the space of tempered functions on finitely generated Abelian groups”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2016, no. 5(36), 42–59
2015
6.
S. S. Platonov, “On spectral synthesis on element-wise compact Abelian groups”, Mat. Sb., 206:8 (2015), 127–152; Sb. Math., 206:8 (2015), 1150–1172
S. S. Platonov, “Some problems of approximation theory of functions on the infinite dimensional torus: analogues of Jackson theorems”, Algebra i Analiz, 26:6 (2014), 99–120; St. Petersburg Math. J., 26:6 (2015), 933–947
S. S. Platonov, “Spectral synthesis in a space of exponential growth functions on finitely generated abelian groups”, Algebra i Analiz, 24:4 (2012), 182–200; St. Petersburg Math. J., 24:4 (2013), 663–675
S. S. Platonov, “Invariant subspaces in some function spaces on the light cone in $\mathbb R^3$”, Mat. Sb., 203:6 (2012), 101–130; Sb. Math., 203:6 (2012), 864–892
S. S. Platonov, “Инвариантные подпространства в функциональных пространствах медленного роста на световом конусе в $R^{3}$”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 2011, no. 18, 21–60
2010
14.
С. С. Platonov, “Spectral synthesis in some topological vector spaces of functions”, Algebra i Analiz, 22:5 (2010), 154–185; St. Petersburg Math. J., 22:5 (2011), 813–833
S. S. Platonov, E. N. Syromolotov, “О продолжении операторов обобщенного сдвига Данкля”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 2009, no. 16, 60–77
16.
S. S. Platonov, “Some problems in the theory of approximation of functions on compact homogeneous manifolds”, Mat. Sb., 200:6 (2009), 67–108; Sb. Math., 200:6 (2009), 845–885
S. S. Platonov, “Bessel generalized translations and some problems of approximation theory for functions on the half-line”, Sibirsk. Mat. Zh., 50:1 (2009), 154–174; Siberian Math. J., 50:1 (2009), 123–140
S. S. Platonov, E. S. Belkina, “Equivalence of $K$-functionals and moduli of smoothness constructed by generalized Dunkl translations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 8, 3–15; Russian Math. (Iz. VUZ), 52:8 (2008), 1–11
S. S. Platonov, “Analog of the Whittaker–Kotelnikov–Shannon Theorem from the Point of View of Fourier–Bessel Analysis”, Mat. Zametki, 83:2 (2008), 264–272; Math. Notes, 83:2 (2008), 238–245
S. S. Platonov, “Bessel harmonic analysis and approximation of functions on the half-line”, Izv. RAN. Ser. Mat., 71:5 (2007), 149–196; Izv. Math., 71:5 (2007), 1001–1048
S. S. Platonov, “Обобщенные сдвиги Бесселя и некоторые обратные теоремы теории приближения функций на полупрямой”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 2007, no. 14, 44–57
2005
22.
S. S. Platonov, “The Fourier transform of functions satisfying the Lipschitz condition on rank 1 symmetric spaces”, Sibirsk. Mat. Zh., 46:6 (2005), 1374–1387; Siberian Math. J., 46:6 (2005), 1108–1118
S. S. Platonov, “Разложение по собственным функциям для некоторых функционально-дифференциальных операторов”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 2004, no. 11, 14–34
S. S. Platonov, “Преобразование Фурье функций удовлетворяющих условию Липшица, на плоскости Лобачевского”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 2003, no. 10, 31–40
2002
25.
S. S. Platonov, “Invariant subspaces in some function spaces on symmetric spaces. III”, Izv. RAN. Ser. Mat., 66:1 (2002), 167–202; Izv. Math., 66:1 (2002), 165–200
S. S. Platonov, “On a determination of entire functions of exponential type on homogeneous manifolds”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 2, 60–68; Russian Math. (Iz. VUZ), 45:2 (2001), 56–63
27.
S. S. Platonov, “Обобщенные сдвиги Бесселя и некоторые задачи теории приближений функций в метрике $L_{2}$. II”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 2001, no. 8, 20–36
S. S. Platonov, “On Equivalent Normings in the Spaces $H_p^r$ on Compact Homogeneous Spaces”, Mat. Zametki, 68:6 (2000), 898–909; Math. Notes, 68:6 (2000), 760–769
S. S. Platonov, “Обобщенные сдвиги Бесселя и некоторые задачи теории приближений функций в метрике $L_{2}$. I”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 2000, no. 7, 70–83
S. S. Platonov, “Approximation of functions in the $L_2$-metric on noncompact symmetric spaces of rank 1”, Algebra i Analiz, 11:1 (1999), 244–270; St. Petersburg Math. J., 11:1 (2000), 183–201
S. S. Platonov, “Сходимость и секвенциальная сходимость в некоторых функциональных топологических векторных пространствах”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 1999, no. 6, 68–91
1998
34.
S. S. Platonov, “Invariant subspaces in some function spaces on symmetric spaces. II”, Izv. RAN. Ser. Mat., 62:2 (1998), 131–168; Izv. Math., 62:2 (1998), 339–374
S. S. Platonov, “Invariant subspaces in functional spaces of polynomial growth on $\mathbb{R}^{N}$”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 1997, no. 4, 105–124
S. S. Platonov, “О классах Никольского — Бесова на компактных симметрических пространствах ранга 1”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 1996, no. 3, 118–137
41.
S. S. Platonov, “О спектральном синтезе в одном топологическом векторном пространстве целых функций”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 1996, no. 3, 97–117
1995
42.
S. S. Platonov, “On approximation on compact symmetric spaces of rank $1$”, Dokl. Akad. Nauk, 342:4 (1995), 455–457
43.
S. S. Platonov, “Invariant subspaces of some function spaces on symmetric spaces. I”, Izv. RAN. Ser. Mat., 59:5 (1995), 127–172; Izv. Math., 59:5 (1995), 1007–1050
S. S. Platonov, “Инвариантные подпространства в некоторых функциональных пространствах на евклидовом пространстве”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 1995, no. 2, 92–112
S. S. Platonov, “Подпространства, инвариантные относительно обобщенных сдвигов Якоби”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 1995, no. 2, 71–91
1993
46.
S. S. Platonov, “О взаимно однозначном соответствии между инвариантными подпространствами в некоторых пространствах”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 1993, no. 1, 54–60
1992
47.
S. S. Platonov, “Spectral synthesis on symmetric spaces of rank 1”, Algebra i Analiz, 4:4 (1992), 174–187; St. Petersburg Math. J., 4:4 (1993), 777–788
S. S. Platonov, “Invariant subspaces in some function spaces on symmetric spaces of
rank $1$. Symplectic and special cases”, Dokl. Akad. Nauk, 322:2 (1992), 243–247; Dokl. Math., 45:1 (1992), 73–77
S. S. Platonov, “Subspaces that are invariant with respect to generalized translations”, Mat. Zametki, 47:6 (1990), 91–101; Math. Notes, 47:6 (1990), 588–595
50.
S. S. Platonov, “Invariant subspaces in some function spaces on the group of motions in the Euclidean plane”, Sibirsk. Mat. Zh., 31:3 (1990), 135–146; Siberian Math. J., 31:3 (1990), 472–481
S. S. Platonov, “Invariant subspaces in some function spaces on symmetric spaces of
rank $1$”, Dokl. Akad. Nauk SSSR, 303:4 (1988), 797–799; Dokl. Math., 38:3 (1989), 606–608
S. S. Platonov, “Invariant subspaces in certain function spaces on $n$-dimensional Lobachevsky space”, Mat. Sb. (N.S.), 137(179):4(12) (1988), 435–461; Math. USSR-Sb., 65:2 (1990), 439–464
S. S. Platonov, “An axiomatic description of the algebra $H^\infty(D)$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 9, 71–74; Soviet Math. (Iz. VUZ), 31:9 (1987), 87–90
1986
54.
S. S. Platonov, “Subspaces of entire functions invariant with respect to differentiation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1986, no. 4, 49–56; Soviet Math. (Iz. VUZ), 30:4 (1986), 64–72
55.
S. S. Platonov, “Subspaces invariant under generalized shifts”, Mat. Zametki, 39:4 (1986), 576–585; Math. Notes, 39:4 (1986), 316–321
1984
56.
S. S. Platonov, “Invariant subspaces in certain function spaces on an elementary solvable Lie group”, Mat. Zametki, 35:1 (1984), 19–30; Math. Notes, 35:1 (1984), 12–18
Full list of publications
