Proceedings o f th e St. Petersbur g Mathematical Societ y Volume X

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American Mathematica l Societ y

TRANSLATIONS Series 2 • Volum e 21 4

Proceedings o f th e St. Petersbur g Mathematical Societ y Volume X

N. N . Uraltsev a Editor

American Mathematica l Societ y Providence, Rhod e Islan d

http://dx.doi.org/10.1090/trans2/214

EDITORIAL COMMITTE E

AMS Subcommitte e Robert D . MacPherson

Grigorii A . Margulis James D . Stasheff (Chair )

ASL Subcommitte e Steffe n Lemp p (Chair ) IMS Subcommitte e Mar k I . Freidlin (Chair )

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MATEMATM^ECKOrO OBIIIECTBA, TO M 1 0

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This wor k wa s originally publishe d i n Russi a b y th e Publ ishe r T a m a r a Rozhkovskaya , Novosibirsk, Russi a unde r th e t i t l e "Tpy^b i CaHKT-IIeTep6yprcKor o MaTeMaTKrqecKor o 06mecTBa, T . 10 " © CaHKT-IIeTep6yprcKo e MaTeMaTprqecKo e OGniecTBO . T h e presen t t rans la t ion wa s created unde r licens e fo r th e America n Mathemat ica l Societ y an d i s pub -lished b y permission .

2000 Mathematics Subject Classification. P r imar y 00B55 .

ISBN 0-8218-3861- X ISSN 0065-929 0

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Contents

Dynamical invers e proble m fo r th e Schrodinge r equatio n (BC-method ) S. A . AVDONI N AN D M . I . BELISHE V 1

On th e Lyapuno v dimensio n o f th e attracto r o f th e Chiriko v dissipativ e mapping G. A . LEONO V AN D M . S . POLTINNIKOV A 1 5

On solution s t o th e Dirichle t proble m fo r a n equatio n wit h p-Laplacian i n a spherical laye r A. I . NAZARO V 2 9

Asymptotic analysi s o f an arbitrar y spatia l syste m o f thin rod s S. A . NAZARO V AN D A . S . SLUTSKI I 5 9

Kubo-Martin-Schwinger state s o n th e grou p GL (oo) an d admissibl e representations o f GL(oo) x

N. I . NESSONO V 10 9

C1-Version o f Arnold' s conjectur e abou t limi t set s o f domain s S. Yu . PILYUGI N 16 7

#2-Optimal quadratur e formul a wit h Chebyshe v weigh t o f the secon d kind : Estimate fo r th e remainde r ter m B. A . SAMOKIS H 17 7

Calculus o f pseudodifferentia l boundar y valu e problem s o n manifold s wit h smooth edge s O. V . SARAFANO V 18 3

Garal'd Isidorovic h Natanso n 0 . L . VINOGRADOV , V . V . ZHUK , V . L . FAINSHMIDT , AN D V . P .

KHAVIN 23 7

Leonid Vital'evic h Kantorovic h an d computationa l mathematic s 1. K . DAUGAVET , V . M . RYABOV , AN D B . A . SAMOKIS H 25 3

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Titles i n Thi s Serie s

214 N . N . Uraltseva , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society , Volume X

213 Ernes t Vinberg , Editor , Li e group s an d invarian t theor y

212 V . M . Buchstabe r an d I . M . Krichever , Editors , Geometry , topology , an d

mathematical physic s

211 K . Nomizu , Editor , Selecte d paper s o n analysi s an d differentia l equation s

210 S . G . Gindikin , Editor , Li e group s an d symmetri c spaces . I n memor y o f F . I .

Karpelevich

209 N . N . Uraltseva , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society ,

Volume I X

208 M . V . Karasev , Editor , Asymptoti c method s fo r wav e an d quantu m problem s

207 Yu . M . Suhov , Editor , Analyti c method s i n applie d probabilit y

206 M . A . Shubi n an d M . S . Agranovich , Editors , Partia l differentia l equation s (Mar k

Viskik's Seminar )

205 N . N . Uraltseva , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society ,

Volume VII I

204 K . Nomizu , Editor , Selecte d paper s o n classica l analysi s

203 N . N . Uraltseva , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society ,

Volume VI I

202 V . Turae v an d A . Vershik , Editors , Topology , ergodi c theory , rea l algebrai c geometry .

Rokhlin's memoria l

201 Michae l Semenov-Tian-Shansky , Editor , L . D . Faddeev' s semina r o n mathematica l physics

200 L . Lerman , G . Polotovskii , an d L . Shilnikov , Editors , Method s o f qualitativ e

theory o f differentia l equation s an d relate d topic s

199 N . N . Uraltseva , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society ,

Volume V I

198 R . A . Minlos , Seny a Shlosman , an d Yu . M . Suhov , Editors , O n Dobrushin' s way .

From probabilit y theor y t o statistica l physic s

197 Vladimi r Arnold , M a x i m Kontsevich , an d Anto n Zorich , Editors , Pseudoperiodi c

topology

196 Ya . Eliashberg , D . Fuchs , T . Rat iu , an d A . Weinste in , Editors , Norther n

California symplecti c geometr y semina r

195 O . V . Belegrade k e t al. , Mode l Theor y an d Application s

194 A . Astashkevic h an d S . Tabachnikov , Editors , Differentia l Topology , Infinite-Dimensional Li e Algebras , an d Application s (D . B . Fuchs ' 60t h Anniversar y Collection)

193 N . N . Uraltseva , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society , Volume V

192 Le v Beklemishev , Mat i Pentus , an d Nikola i Vereshchagin , Provability , Complexity, Grammar s

191 A . Yu . Morozo v an d M . A . Olshanetsky , Editors , Mosco w Semina r i n

Mathematical Physic s

190 S . Tabachnikov , Editor , Differentia l an d Symplecti c Topolog y o f Knot s an d Curve s

189 V . Buslaev , M . Solomyak , an d D . Yafaev , Editors , Differentia l Operator s an d

Spectral Theor y (M . Sh . Birman' s 70t h anniversar y collection )

188 O . A . Ladyzhenskaya , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society , Volume I V 187 M . V . Karasev , Editor , Coheren t Transform , Quantization , an d Poisso n Geometr y

TITLES I N THI S SERIE S

186 A . Khovanskii , A . Varchenko , an d V . Vassiliev , Editors , Geometr y o f Differentia l Equations

185 B . Feigi n an d V . Vassiliev , Editors , Topic s i n Quantu m Group s an d Finite-Typ e

Invariants (Mathematic s a t th e Independen t Universit y o f Moscow )

184 Pete r Kuchmen t an d Vladimi r Lin , Editors , Voronez h Winte r Mathematica l School s

(Dedicated t o Seli m Krein )

183 K . Nomizu , Editor , Selecte d Paper s o n Harmoni c Analysis , Groups , an d Invariant s

182 V . E . Zakharov , Editor , Nonlinea r Wave s an d Wea k Turbulenc e

181 G . I . Olshanski , Editor , Kirillov' s Semina r o n Representatio n Theor y

180 A . Khovanskii , A . Varchenko , an d V . Vassiliev , Editors , Topic s i n Singularit y

Theory

179 V . M . Buchstabe r an d S . P . Novikov , Editors , Solitons , Geometry , an d Topology :

On th e Crossroa d

178 V . Kreinovic h an d G . Mints , Editors , Problem s o f Reducin g th e Exhaustiv e Searc h

177 R . L . Dobrushin , R . A . Minlos , M . A . Shubin , an d A . M . Vershik , Editors ,

Topics i n Statistica l an d Theoretica l Physic s (F . A . Berezi n Memoria l Volume )

176 E . V . Shikin , Editor , Som e Question s o f Differentia l Geometr y i n th e Larg e

175 R . L . Dobrushin , R . A . Minlos , M . A . Shubin , an d A . M . Vershik , Editors ,

Contemporary Mathematica l Physic s (F . A . Berezi n Memoria l Volume )

174 A . A . Bolibruch , A . S . Merkur'ev , an d N . Yu . Netsve taev , Editors , Mathematic s

in St . Petersbur g

173 V . Kharlamov , A . Korchagin , G . Polotovskii , an d O . Viro , Editors , Topolog y o f

Real Algebrai c Varietie s an d Relate d Topic s

172 K . Nomizu , Editor , Selecte d Paper s o n Numbe r Theor y an d Algebrai c Geometr y

171 L . A . Bunimovich , B . M . Gurevich , an d Ya . B . Pesin , Editors , Sinai' s Mosco w

Seminar o n Dynamica l System s

170 S . P . Novikov , Editor , Topic s i n Topolog y an d Mathematica l Physic s

169 S . G . Gindiki n an d E . B . Vinberg , Editors , Li e Group s an d Li e Algebras : E . B .

Dynkin's Semina r

168 V . V . Kozlov , Editor , Dynamica l System s i n Classica l Mechanic s

167 V . V . Lychagin , Editor , Th e Interpla y betwee n Differentia l Geometr y an d Differentia l

Equations

166 O . A . Ladyzhenskaya , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society ,

Volume II I

165 Yu . Ilyashenk o an d S . Yakovenko , Editors , Concernin g th e Hilber t 16t h Proble m

164 N . N . Uraltseva , Editor , Nonlinea r Evolutio n Equation s

163 L . A . Bokut' , M . Hazewinkel , an d Yu . G . Reshetnyak , Editors , Thir d Siberia n

School 'Algebr a an d Analysis "

162 S . G . Gindikin , Editor , Applie d Problem s o f Rado n Transfor m

161 K . Nomizu , Editor , Selecte d Paper s o n Analysis , Probability , an d Statistic s

160 K . Nomizu , Editor , Selecte d Paper s o n Numbe r Theory , Algebrai c Geometry , an d

Differential Geometr y

159 O . A . Ladyzhenskaya , Editor , Proceeding s o f th e St . Petersbur g Mathematica l Society ,

Volume I I

158 A . K . Kelmans , Editor , Selecte d Topic s i n Discret e Mathematics : Proceeding s o f th e Moscow Discret e Mathematic s Semina r 1972-199 0

For a complet e lis t o f t i t le s i n thi s series , visi t th e AMS Bookstor e a t w w w . a m s . o r g / b o o k s t o r e / .