generalized functions,
integral transforms,
differential equations,
tauberian theorems,
complex analysis.
Subject:
Tauberian theory for distributions. Boundary properties of holomorphic functions. Asymptotic properties of solutions of differential equations. Automodel asymptotic in quantum field theory.
Biography
1971 — graduated from Moscow State University. 1971–1974 — postgraduate in Steklov Mathematical Institute. From 1974 up to now — collaborator of the Institute. 1974 — candidate degree. 1983 — doctor degree.
Main publications:
Zavyalov B. I. Ob asimptoticheskikh svoistvakh funktsii, golomorfnykh v trubchatykh konusakh // Matematicheskii sbornik, 1988, 136 (178), # 1 (5).
Vladimirov V. S., Drozhzhinov Yu. N., Zavyalov B. I. Mnogomernye tauberovy teoremy dlya obobschennykh funktsii. Moskva: Nauka, 1986.
Drozhzhinov Yu. N., Zavyalov B. I. Teoremy tauberova tipa dlya obobschennoi multiplikativnoi svertki // Izvestiya RAN, ser. matem., 2000, 64 (1), 37–94.
Yu. N. Drozhzhinov, B. I. Zavialov, “Comparison Tauberian theorems and hyperbolic operators with constant coefficients”, Ufa Math. Journal, 7:3 (2015), 47–53
2.
Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter group”, Proc. Steklov Inst. Math., 285 (2014), 99–119
3.
Yu. N. Drozhzhinov, B. I. Zavialov, “Generalized functions asymptotically homogeneous with respect to one–parametric group at origin”, Ufa Mathematical Journal, 5:1 (2013), 17–35
4.
Yu. N. Drozhzhinov, B. I. Zav'yalov, “Asymptotically homogeneous solutions of differential equations whose symbols are polynomials quasi-homogeneous with respect to one-parameter groups with generators containing a nilpotent component”, Dokl. Math., 88:2 (2013), 590–592
5.
Yu. N. Drozhzhinov, B. I. Zavialov, “Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups”, Izv. Math., 76:3 (2012), 466–516
6.
Yu. N. Drozhzhinov, B. I. Zavialov, “Homogeneous Generalized Functions with Respect to One-Parametric Group”, p-Adic Numbers, Ultrametric Analysis and Applications, 4:1 (2012), 64–75
Yu. N. Drozhzhinov, B. I. Zav'yalov, “Generalized functions asymptotically homogeneous along the unstable degenerated node”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(22) (2011), 68–82
8.
Yu. N. Drozhzhinov, B. I. Zav'yalov, “Asymptotically homogeneous generalized functions along trajectories defined by a general one-parameter transformation group”, Dokl. Math., 82:3 (2010), 874–877
9.
Yu. N. Drozhzhinov, B. I. Zavyalov, “Asimptoticheski odnorodnye obobschennye funktsii v nule i uravneniya v svertkakh s yadrami, simvoly kotorykh – kvaziodnorodnye mnogochleny”, Dokl. RAN, 426:3 (2009), 300–303
Yu. N. Drozhzhinov, B. I. Zavialov, “Generalized functions asymptotically homogeneous along special transformation groups”, Sb. Math., 200:6 (2009), 803–844
11.
Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically quasi-homogeneous generalized functions at the origine”, Ufimsk. Mat. Zh., 1:4 (2009), 24–57
12.
Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically quasi-homogeneous distributions”, Dokl. Math., 78:1 (2008), 503–507
13.
Yu. N. Drozhzhinov, B. I. Zavyalov, “Mnogomernye tauberovy teoremy v nekotorykh modelyakh matematicheskoi fiziki”, Vtoroe rossiisko-armyanskoe soveschanie po matematicheskoi fizike, kompleksnomu analizu i smezhnym voprosam, Tezisy dokladov (Moskva, MIAN, 5–11 oktyabrya 2008 g.), 2008, 30–31
14.
Yu. N. Drozhzhinov, B. I. Zavialov, “Applications of Tauberian theorems in some problems in mathematical physics”, Theoret. and Math. Phys., 157:3 (2008), 1678–1693
15.
J. Contemp. Math. Anal., 41:5 (2006), 9–15
16.
J. Contemp. Math. Anal., 41:6 (2006), 20–29
17.
Yu. N. Drozhzhinov, B. I. Zavyalov, “Asymptotically homogeneous generalized functions”, Publ. Inst. Math. (Beograd) (N.S.), 80(94) (2006), 97–108
18.
Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically homogeneous generalized functions and boundary properties of functions holomorphic in tubular cones”, Izv. Math., 70:6 (2006), 1117–1164
19.
Yu. N. Drozhzhinov, B. I. Zavialov, “Introduction to the theory of generalized functions”, Lekts. Kursy NOC, 5, Steklov Math. Inst., RAS, Moscow, 2006, 3–162
20.
Yu. N. Drozhzhinov, B. I. Zavyalov, “Asimptoticheski odnorodnye obobschennye funktsii v sfericheskom predstavlenii i nekotorye primeneniya”, Dokl. RAN, 405:1 (2005), 18–21
Yu. N. Drozhzhinov, B. I. Zavyalov, “Quasi-asymptotics and spherical representation of generalized functions”, Dokl. RAN, 398:5 (2004), 591–594
22.
Yu. N. Drozhzhinov, B. I. Zavyalov, “Ob odnoi mnogomernoi teoreme tauberova tipa dlya obobschennykh funktsii so znacheniyami v banakhovykh prostranstvakh”, Dokl. RAN, 391:2 (2003), 158–161
Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Tauberian theorems for Banach-space valued generalized functions”, Sb. Math., 194:11 (2003), 1599–1646
24.
V. S. Vladimirov, Yu. N. Drozhzhinov, B. I. Zavyalov, “Tauberian theorems for generalized functions in a scale of regularly varying functions and functionals”, Publ. Inst. Math. (Beograd) (N.S.), 71(85), Dédié à Jovan Karamata (2002), 123–132
Yu. N. Drozhzhinov, B. I. Zavyalov, “Tauberian-type theorems for generalized functions in the scale of self-similar functionals”, Dokl. RAN, 383:2 (2002), 156–160
Yu. N. Drozhzhinov, B. I. Zavialov, “Tauberian theorems for generalized functions with values in Banach spaces”, Izv. Math., 66:4 (2002), 701–769
27.
Yu. N. Drozhzhinov, B. I. Zavialov, “Tauberian theorem for generalized multiplicative convolutions”, Izv. Math., 64:1 (2000), 35–92
28.
Yu. N. Drozhzhinov, B. I. Zavialov, “Wiener-Type Tauberian Theorems for Generalized Functions on the Half-Axis”, Proc. Steklov Inst. Math., 228 (2000), 43–51
29.
Yu. N. Drozhzhinov, B. I. Zavyalov, “Wiener-type theorems for generalized functions, and the integral Stieltjes transform”, Dokl. RAN, 363:2 (1998), 156–159
Yu. N. Drozhzhinov, B. I. Zavialov, “A Wiener-type Tauberian theorem for generalized functions of slow growth”, Sb. Math., 189:7 (1998), 1047–1086
32.
Yu. N. Drozhzhinov, B. I. Zavialov, “Local Tauberian theorems in spaces of distributions related to cones, and their applications”, Izv. Math., 61:6 (1997), 1171–1214
33.
Yu. N. Drozhzhinov, B. I. Zavyalov, “On the noncompensation of singularities of functions that are holomorphic in tubular cones”, Dokl. RAN, 346:1 (1996), 11–12
34.
Yu. N. Drozhzhinov, B. I. Zavyalov, “Quasi-asymptotic expansion of a measure”, Publ. Inst. Math. (Beograd) (N.S.), 58(72), Slobodan Aljančić memorial volume (1995), 153–161
35.
Yu. N. Drozhzhinov, B. I. Zavialov, “Theorems of Hardy–Littlewood type for signed measures on a cone”, Sb. Math., 186:5 (1995), 675–693
36.
Yu. N. Drozhzhinov, B. I. Zavialov, “A Tauberian theorem for quasiasymptotic decompositions of measures with supports in the positive octant”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 185–209
37.
Yu. N. Drozhzhinov, B. I. Zavialov, “A theorem on the division of generalized functions by a homogeneous function with preservation of quasiasymptotics, and its application”, Proc. Steklov Inst. Math., 203 (1995), 67–77
38.
V. S. Vladimirov, Yu. N. Drozzinov, B. I. Zavialov, “Tauberian theorems for distributions”, International Symposium in Memory of Hua Loo Keng (Beijing, 1988), Vol. II, Springer, Berlin, 1991, 301–311
39.
Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional tauberian comparison theorems for holomorphic functions of bounded argument”, Math. USSR-Izv., 39:3 (1992), 1097–1112
40.
Yu. N. Drozzinov, B. I. Zavialov, “On multidimensional generalizations of regularly varying functions and Tauberian and Abelian theorems”, Publ. Inst. Math. (Beograd) (N.S.), Proceedings of the Third Annual Meeting of the International Workshop in Analysis and its Applications, 48(62), 1990, 69–72
41.
V. S. Vladimirov, Yu. N. Drožžinov, B. I. Zavialov, “Multi-dimensional Tauberian theorems for distributions”, Generalized functions and convergence (Katowice, 1988), World Sci. Publ., Teaneck, NJ, 1990, 265–277
42.
Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Abelian and Tauberian comparison theorems”, Math. USSR-Sb., 68:1 (1991), 85–110
43.
B. I. Zavialov, “On the asymptotic properties of functions holomorphic in tubular cones”, Math. USSR-Sb., 64:1 (1989), 97–113
44.
B. I. Zavyalov, “On the asymptotic properties of functions that are holomorphic in tubular cones”, Dokl. AN SSSR, 294:5 (1987), 1048–1050
45.
V. S. Vladimirov, Yu. N. Drozhzhinov, B. I. Zavialov, “Tauberian theorems for generalized functions and their applications”, Proc. Steklov Inst. Math., 175 (1988), 107–116
46.
Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotic properties of some classes of generalized functions”, Math. USSR-Izv., 26:1 (1986), 77–131
47.
Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Tuberian comparison theorems for generalized functions in cones”, Math. USSR-Sb., 54:2 (1986), 499–524
48.
V. S. Vladimirov, Yu. N. Drozzinov, B. I. Zavialov, “Tauberian theorems for distributions”, Complex analysis and applications '81 (Varna, 1981), Publ. House Bulgar. Acad. Sci., Sofia, 1984, 524–532
49.
Yu. N. Drozhzhinov, B. I. Zavyalov, “Teoremy sravneniya tauberova tipa”, Dokl. AN SSSR, 279:3 (1984), 532–535
V. S. Vladimirov, Yu. N. Drozhzhinov, B. I. Zavialov, “Theorems of Tauberian type for generalized functions”, Proc. Steklov Inst. Math., 163 (1985), 53–60
51.
Yu. N. Drozhzhinov, B. I. Zavyalov, “O mnogomernom analoge teoremy Lindelëfa”, Dokl. AN SSSR, 262:2 (1982), 269–270
V. S. Vladimirov, B. I. Zavialov, “Self-similar asymptotic behavior of causal functions and their behavior on the light cone”, Theoret. and Math. Phys., 50:2 (1982), 105–126
53.
V. S. Vladimirov, B. I. Zavyalov, “Avtomodelnaya asimptotika i povedenie na svetovom konuse v kvantovoi teorii polya”, Dokl. AN SSSR, 258:4 (1981), 842–846
54.
V. S. Vladimirov, Yu. N. Drozhzhinov, B. I. Zavyalov, “Teoremy tauberova tipa dlya obobschennykh funktsii”, Obobschennye funktsii i ikh primeneniya v matematicheskoi fizike (Moskva, 1980), VTs AN SSSR, M., 1981, 125–134
55.
B. I. Zavialov, “Jost–Lehmann–Dyson representation in the spaces $S'_\alpha$”, Theoret. and Math. Phys., 49:2 (1981), 945–951
56.
V. S. Vladimirov, B. I. Zav'yalov, “Tauberian theorems in quantum field theory”, J. Soviet Math., 16:6 (1981), 1487–1509
57.
Yu. N. Drozhzhinov, B. I. Zavialov, “Tauberian theorems for generalized functions with supports in cones”, Math. USSR-Sb., 36:1 (1980), 75–86
58.
V. S. Vladimirov, B. I. Zavialov, “Tauberian theorems in quantum field theory”, Theoret. and Math. Phys., 40:2 (1979), 660–677
59.
Yu. N. Drozhzhinov, B. I. Zavialov, “Quasi-asymptotics of generalized functions and Tauberian theorems in the complex domain”, Math. USSR-Sb., 31:3 (1977), 329–345
60.
B. I. Zavialov, “Bjorken asymptotic behavior of deep inelastic scattering form factors and the general principles of field theory”, Theoret. and Math. Phys., 33:3 (1977), 1040–1046
61.
B. I. Zavialov, V. B. Trushin, “On the extended $n$-point tube”, Theoret. and Math. Phys., 27:1 (1976), 293–301
62.
B. I. Zavialov, ““Quasiasymptotics” of generalized functions and scaling of electromagnetic form factors”, Theoret. and Math. Phys., 19:2 (1974), 426–432
63.
B. I. Zavialov, “Aling of electromagnetic form factors and the behavior of their Fourier transforms in the neighborhood of the light cone”, Theoret. and Math. Phys., 17:2 (1973), 1074–1081
64.
B. I. Zavialov, “On the behavior of the electromagnetic form factors in the neighborhood of the light cone”, Theoret. and Math. Phys., 16:1 (1973), 672–675
Books
65.
V. S. Vladimirov, Yu. N. Drozzinov, B. I. Zavialov, Tauberian theorems for generalized functions, Mathematics and its Applications (Soviet Series), 10, Kluwer Academic Publishers Group, Dordrecht, 1988 , xvi+293 pp.
66.
V. S. Vladimirov, Yu. N. Drozhzhinov, B. I. Zavyalov, Mnogomernye tauberovy teoremy dlya obobschennykh funktsii, Nauka, M., 1986 , 304 pp.
Proceedings
67.
Yu. N. Drozhzhinov, B. I. Zavyalov, “O suschestvovanii asimptoticheski odnorodnykh reshenii differentsialnykh uravnenii”, Tretya mezhdunarodnaya konferentsiya «Matematicheskaya fizika i ee prilozheniya» (Rossiya, g. Samara, 27 avgusta – 1 sentyabrya 2012 g.), Samarskii gosudarstvennyi tekhnicheskii universitet, 2012, 121–122
68.
B. I. Zavyalov, “Asimptoticheski odnorodnye obobschennye funktsii”, Vtoroe rossiisko-armyanskoe soveschanie po matematicheskoi fizike, kompleksnomu analizu i smezhnym voprosam, Tezisy dokladov (Moskva, MIAN, 5–11 oktyabrya 2008 g.), 2008, 40–41
69.
B. I. Zavyalov, “Asimptoticheski odnorodnye obobschennye funktsii”, Mezhdunarodnaya konferentsiya po matematicheskoi fizike i ee prilozheniyam, Tezisy dokladov (Samara, 8–13 sentyabrya 2008 g.), 2008, 76
Personalia
70.
V. S. Vladimirov, I. V. Volovich, A. K. Gushchin, Yu. N. Drozhzhinov, V. V. Zharinov, B. I. Zav'yalov, V. A. Il'in, G. I. Marchuk, V. P. Mikhailov, E. I. Moiseev, S. M. Nikol'skii, B. V. Pal'tsev, “Aleksei Alekseevich Dezin (obituary)”, Russian Math. Surveys, 64:3 (2009), 553–560
71.
I. V. Volovich, A. K. Gushchin, A. A. Dezin, Yu. N. Drozhzhinov, V. V. Zharinov, B. I. Zavyalov, V. A. Il'in, V. M. Millionshchikov, V. N. Mikhailov, A. G. Sergeev, “Vladimirov Vasilii Sergeevich (70-th birthday tribute)”, Differential Equations, 29:2 (1993), 305–313
72.
A. A. Logunov, A. A. Slavnov, O. I. Zavialov, O. A. Khrustalev, V. P. Mikhailov, I. V. Volovich, A. K. Gushchin, Yu. N. Drozhzhinov, V. V. Zharinov, B. I. Zavialov, A. G. Sergeev, V. P. Pavlov, I. Ya. Aref'eva, Yu. A. Tserkovnikov, “The 70th birthday of V. S. Vladimirov”, Theoret. and Math. Phys., 94:1 (1993), 1–2
73.
V. S. Vladimirov, A. K. Gushchin, A. A. Dezin, Yu. N. Drozhzhinov, B. I. Zavialov, V. M. Millionshchikov, “Valentin Petrovich Mikhailov (on his sixtieth birthday)”, Russian Math. Surveys, 46:4 (1991), 207–209
74.
V. S. Vladimirov, A. K. Gushchin, A. A. Dezin, Yu. N. Drozhzhinov, V. I. Zavialov, V. M. Millionshchikov, Differ. Uravn., 27:4 (1991), 725–730
Critic, bibliography
75.
Yu. Drozhzhinov, B. Zavialov, “Recent developments in mathematical physics. Ed. P. Urban. Wien–New York, Springer, 1973, VI+610 pp. (Book review)”, U.S.S.R. Comput. Math. Math. Phys., 14:5 (1974), 261–262
Асимптотические однородные обобщённые функции Yu. N. Drozhzhinov, B. I. Zavialov Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS November 24, 2011 11:00
Асимптотически однородные обобщённые функции Yu. N. Drozhzhinov, B. I. Zavialov Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS October 6, 2005
8.
Асимптотически однородные обобщенные функции Yu. N. Drozhzhinov, B. I. Zavialov Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS November 25, 2004
Books in Math-Net.Ru
Yu. N. Drozhzhinov, B. I. Zavialov, Introduction to the theory of generalized functions, Lekts. Kursy NOC, 5, 2006, 164 с. http://mi.mathnet.ru/book647
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