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1 Mah-NeRu A Rua aheaca ora R F Shaoya S M Kureo О a race oeraor Berga ye aayc ace Sege doa of he ecod ye PFMT 5 Iue ( Ue of he a-rua aheaca ora Mah-NeRu e ha you have read ad agreed o hee er of ue h://wwwaheru/eg/agreee owoad dea: IP: Ar 8 4:45:4

2 Проблемы физики математики и техники (3 5 УДК МАТЕМАТИКА ОБ ОПЕРАТОРЕ СЛЕДА В АНАЛИТИЧЕСКИХ ПРОСТРАНСТВАХ БЕРГМАНА В ОБЛАСТЯХ ЗИГЕЛЯ ВТОРОГО ТИПА РФ Шамоян СМ Куриленко Брянский государственный университет Брянск Россия ОN A TRACE OPERATOR IN BERGMAN TYPE ANALYTIC SPACES IN SIEGEL OMAINS OF THE SECON TYPE RF Shaoya SM Kureo Brya Sae Uvery Brya Rua Получен новый точный результат для оператора следа в аналитических пространствах Бергмана на произведениях областей Зигеля второго типа этот результат обобщает ранее известные результаты в областях менее общего типа Это первые результаты такого рода для областей данного типа Ключевые слова: следы пространства Зигеля аналитические функции пространства Бергмана A ew har reu for a race oeraor aayc Berga ace roduc of Sege doa of he ecod ye exedg revouy ow aero e geera doa rovded Thee are he fr reu of h ye for uch a ye roducdoa Keyword: Trace Sege doa aayc fuco Berga-ye ace Maheac Subec Cafcao (: Prary 4B5 Secodary 4B3 Iroduco The o caca exae of he o yca bouded Sege doa a bouded rcy eudocovex doa Ω wh ooh boudary C a u ba B = { z: z < } The bac fac of he heory of aayc fuco by each varabe roduc of u ba B B were deveoed recey [9] [] [8] I aura o oe varou robe eve ore geera uao aey o coder varou robe roduc of ore geera Sege doa C I a weow fac ha roduc of bouded rcy eudocovex Ω doa C are aga bouded ad eudocovex ad he aer [] wa robaby he fr oe where eroao roere of aayc fuco o uch roduc doa Ω Ω were uded (ee ao rece aer [4] ad referece here Laer varou reu roduc of uch eudocovex doa aeared eraure (ee for exae [] ad referece here The aura queo o coder roduc of eve ore geera ubouded Sege ad bouded Sege doa C uaeouy ( very arcuar cae a e oyd Ad he o geera exae here are geera Sege doa of he ecod ye (drec geerazao of bouded rcy eudocovex ad ubouded ubuar doa over yerc coe uaeouy aey Ω Ω C Noe for = cae hee geera Sege doa of he ecod ye C were uded before (ee for exae [] [] [6] [9] ad [6] ad varou referece here Th aer a couao of a og ere of aer of he fr auhor o race aayc fuco ace o roduc doa The a goa of h aer o ry o fd coee aaogue of our revou har reu o race of aayc fuco ace a u ba (ad roduc of u ba B B C ore geera cae of Sege doa of ecod ye (ad eve roduc of uch doa Naey h oe we a o exed our har reu o a race oeraor Berga ace fro [] I [] gve for he u ba of C cae We ed o exed ha reu o he cae of geera Sege doa of he ecod ye See ao for reaed reu o race [7] [4] [] [] [8] ad referece here The bae of a our roof are roere of Berga roeco Sege doa of he ecod ye gve [] [] ad [6] [9] The eae of Berga ere ad he Berga rereeao forua fro [] [] ad [6] [9] are ao ayg a ora roe our roof beow Noe addo o he argue we ued h aer are very coe o he argue whch were ued before [4] ad [7] [] e geera doa Le u eo [3] [4] [7] where recey oe ew har reu o roduc of he o yca bouded ad ubouded Sege doa of he ecod ye (bouded rcy eudocovex ad ubuar doa over yerc coe were ao obaed We deoe varou coa a uua by C or c wh dexe We fay eo ao [] where race heore cera Shaoya RF Kureo SM 5 83

3 RF Shaoya SM Kureo uuua doa were roved We aer he reader our exoo oee echy Ad he reao here ha a our roof have are wh arae aero ad roof er doa Noao defo ad reare We fr reca oe bac fac o Sege doa of he ecod ye ad eabh bac oao o foruae our a heore Sege doa of he ecod ye ad roduc of uch Sege doa A fac we dcae beow ca be ee [] [] [3] [6] ad [9] Reca fr he exc forua for he Berga ere fuco ow for very few doa The exc for ad zero of he Berga ere fuco for Harog doa ad Harog ye doa (Cara-Harog doa were foud oy recey O he oher had rcy eudocovex doa he rce ar of he Berga ere ca be exreed excy by ere coey reaed o he o-caed He-Rarez ere (ee for exae [] [3] [6] [7] ad referece here The Berga ere b( ( ττ ( ττ 3 4 for Sege doa of he ecod ye wa coued excy (ee [] [] [3] [6] [9] I a egra va V a covex hoogeeou oe rreducbe coe of ra R a cougae coe of V coe ad whch ao coa o ragh e ad ha egra he fxed Hera for fro defo of Sege doa(ee beow for defo arcae(ee for dea of h [] [] ad ao a ora aer [3] Th fac wa heavy ued [] [] ouo of evera caca robe Sege doa of he ecod ye We w eed ow oe hor bu ore cocree revew of cera reu fro [] [] o ae h exoo ore coee To be ore rece he auhor [] [] howed ha o hoogeeou Sege doa of ye uder cera codo o araeer he ubace of a weghed cog of hooorhc fuco are reroduced by a cocree weghed Berga ere whch 84 L ace o for a ove we u eoed They ao oba oe adard L eae for weghed Berga roeco h cae The roof ree o drec geerazao of he Pachere-Gd forua for he Berga ace A (ee [] [] We red he reader ha he Sege doa of ye aocaed wh he oe covex hoogeeou rreducbe coe V of ra whch coa o ragh e V R ad a V Hera hoogeeou for F whch ac fro roduc of wo C o C a e of o ( wτ fro C + o ha he dfferece of I w ad he vaue of F o ( τ τ V coe Th doa affe hoogeeou ad we ow houd reca he foowg exreo for he Berga ere of = ( V F Le be a affe-hoogeeou Sege doa of ye Le dv( z or ( d ( z deoe he Lebegue eaure o doa ad e H ( deoe he ace of a hooorhc fuco o The Berga ere gve by he foowg forua (ee [] for ( τ τ ad ( τ 3τ4 b τ τ d q τ τ τ 3τ 4 = τ τ 4 (( ( 3 ( F( ad we u ao for N τ τ ( ( 3 d q b ( τ τ ( τ 3τ 4 = F( τ τ 4 (ee [] [] where wo vecor q = ( q ad d = ( d ad addo = ( (here he dex rug fro o are ecfed va where hee uber are deo of cera ( R ad ( C ubace of he cera caoca decooo of C + ad R va he V coe fro defo of our doa (ee for oe addoa dea abou h [] [] [6] We w ca h fay of re araeer of a Sege doa of he ecod ye They w coay aear a our a heore A uua H ( edowed wh he ooogy of ufor covergece o coac ube of The Berga roeco P of a uua he orhogoa roeco of Hber ace L ( d oo ubace A ( cog of hooorhc fuco Moreover ow P he egra oeraor defed o Hber ace L ( d by he Berga ere bzζ ( whch for our doa wa coued for exae [3] Le r be a rea uber for exae We fx Sce hoogeeou he ζ B( ζζ fuco doe o vah o we ca e weghed L ace a foow r r L ( = L ( b ( ζζ d( ζ < < (ee [] [] Le be a arbrary ove uber The weghed Berga ace w be deoed a uua by r r A ( he aayc ar of L ( wh uua odfcao for = cae (ee [] [] We ao u A = A ( The o-caed weghed Berga roeco P he orhogoa roeco of Hber ace L ( oo A ( Thee fac ca be foud [] [] I roved [] [] ha here ex a rea uber < uch ha A ( = {} f ; ad ha for > P he egra oeraor defed o L ( by he Проблемы физики математики и техники (3 5

4 О a race oeraor Berga ye aayc ace Sege doa of he ecod ye + weghed Berga ere cb ( ζ z I a our wor we ha aue ha > r The or of A ( wh r > r defed by ( r r f = f ( z b ( z z d ( z f A ( r wh uua odfcao for = cae Le furher dv = b ( z z dv( z R z We eed oe aero (ee [] [] [6] aey oe bac fac o Berga ere ad Berga roeco Sege doa of he ecod ye They w be aray ued by u beow roof of our heore Soe roof of hee reare are raher rcae [] [] [6] We dcae for reader advace ha oe aero beow vovg egra ca be eay exeded o - roduc of Sege doa of ecod ye by e acao of oe varabe reu -e by each varabe earaey Th rocedure we- ow uch er cae of oyd (ee for exae [4] [5] Lea Le h L ( Tae ρ>ρ for a arge fxed ρ The he fuco +ρ z G( z = b ( zζ h( ζ d( ζ ρ afe he eae u Gz ( b ( zz ch z ad G H( The foowg ea a coee aaogue of he o-caed Forey-Rud ye eae for our Sege doa of he ecod ye Lea Le α ad be R ( ζ v The we have b +α (( v ( z u b ζ (( z u ( z u dv ( z u < f ad oy f > ad α > ( d q = The foowg ea aoher coee aaogue of he o-caed Forey-Rud ye eae for our Sege doa of he ecod ye (oe hee ye eae are we-ow er doa Lea 3 Le α ad be R ( ζ v The for > ad α > ( d q = b +α (( v ( z u b ζ (( z u ( z u dv ( z u = α = cαb (( ζ v ( ζ v The foowg ea a vero of caca reroducg Berga forua for Berga ace Sege doa of he ecod ye Lea 4 Le r be a vecor of R uch ha r > for a = ad a a rea uber uch ha ( + r < = q The for a R uch ha r > + = r he foowg equay hod Pf = f f A We ea 5 oe oher roere of Berga ere The a eae aero beow a ebeddg heore I reae he o-caed growh ace wh Berga ace (ee ao he coee aaogue of h reu oher er doa [] [] ad [4] [5] Lea 5 Le α R ; α > or α = = The α α b (( ζ v ( z u cαb (( ζ v ( ζ v ad α b (( ζ v + ( ζ v ;( z u + ( z u α cb α (( ζ v ( ζ v for a ( ζ v ( ζ v ( z u ( z u For a r f A ( > r f( z u cb + (( z u ( z u f r for a ( zu o ae fro The foowg reu cruca for he roof of our heore I cocer he boudede of Berga ye roeco weghed Berga ace Noe h fac caca er doa ad ha ao ay acao aayc fuco heory (ee [4] [5] Prooo Le ad r be R uch ha > ad r > = ( d q r r The P bouded fro L ( o A ( f ( d q r ax < < = ( d q ( d q r < = We deoe beow everywhere by ad by he rgh ad he ef ed of he erva for araeer whch ca be ee rooo The foowg aero a bae of roof of heore 3 I rovde a egra rereeao for he ocaed aayc growh ace o Sege doa of he ecod ye Prooo Le r ad be wo vecor of R uch ha Probe of Phyc Maheac ad Techc (3 5 85

5 RF Shaoya SM Kureo > ( d q ; r > + = Le G be H ( o ha G u{ G ( z b = ( z z } < The PG r 86 A = G z The foowg reu exa he rucure of fuco fro Berga ace o Sege doa of he ecod ye I a exeo of a caca heore o aoc decooo of Berga ace he u d o a coex ae (ee for exae [9] ad referece here Prooo 3 Le Sege doa of ye II r > + C be a yerc r R ; The here are wo coa c = c( r ad c = c ( r uch ha for every r f A ( here ex a equece { λ } uch ha = + r α α/ f( z = λ b ( z z b ( z z where { z } a ace ad he foowg eae hod r = r c f λ c f where α a eca fxed vecor deedg o r ad araeer of Sege doa (ee for h vecor [9] Shar heore o race aayc ace of Berga ye o Sege doa ad o roduc of Sege doa of he ecod ye The goa of h a eco o exed he a reu of [] [8] o race gve here for arcuar cae of he u ba o geera hoogeeou Sege doa of he ecod ye We ar however wh oe ereg dcuo reaed wh hee ue Fr we defe ad fx oe roere of Berga-ye ace o roduc of Sege doa of he ecod ye A ( > Thee ace arcuar cae of he u ba are coey reaed o Trace oeraor ad ufucoa aayc fuco ace hgher deo (ee for exae [9] [] [8] ad varou referece here More recey we coder ace of a aayc fuco (aayc by each varabe earaey f( z z H( The we defe for ( R > = he foowg ace o roduc doa We defe fr a ube of Locay egrabe fuco o ( L ( = = ocay egrabe : f = ( f( z z b ( z z dv( z / = / b ( z z dv( z < N ad A = H( L ( May geera ue reaed o varou fucoa ace o roduc doa ca be ee [5] Laer h oc wa deveoed by ay auhor (ee for exae for oe ew aayc ace o roduc doa [8] ad referece here Berga-ye xed or ace roduc of Sege doa of he ecod ye for ( > = are Baach ace ad coee erc for oher vaue of araeer Noe for very arcuar cae whe C + (uer haf ace or whe a u d o a coex ae C ad a = for each fro o hee are we-ow aayc Berga ye ace a oyd or oyhaace (ee [4] [5] ad [8] A aura queo o ry o uderad he rucure of hee ew ereg ace ad arcuar o exed reu obaed for = [] [] o h geera > cae I h aer we coder oy arcuar = cae where = Our a heore are har race heore for hee ace for h arcuar cae I addo ay queo cocerg varou ebeddg bewee uch aayc Berga ye ace wh vecor ao are auray We oe ao he udy of hee ye cae o roduc doa o yca Sege doa (bouded or uboudedbouded rcy eudocovex doa or ubuar doa over yerc coe or oyba wa ared arcuar recey aer of fr auhor ad coauhor (ee [3] [4] [7] We eo ao [] ad [] for oe reu h area Soe ew reu abou hee ace arcuar cae of a oyba ca be ee [8]We w eed he foowg e obervao I oe uao ug by each varabe earaey -e he oe deoa reu we ge a ar reu bu for roduc doa Th obervao ca be aed o varou aero we had above A a exae we oe eay ha for exae baed o a ar of Lea 5 we have (u f( z z z z ( + r ( r + b ( z z b ( z z C( f r = c f( z z b( z z dv( z dv( z where C ( f = u f( z z z z + z z r bz ( z dvz ( + dvz ( = + Проблемы физики математики и техники (3 5

6 О a race oeraor Berga ye aayc ace Sege doa of he ecod ye = bz ( z ( + r Sce C ( f C ( f c f r where A ( + r C ( f = u u f( z b ( z z z z z = + r + bz ( z dvz ( dvz ( = L ( + r b ( z z efg ad A aura ao o coder = cae For = cae hee or w oo e / u f ( z z ( b ( z z dv( z ( b ( z z z for A or ( u ( ( ( f z z b z z b z z dv z ( ( ( for A We defe A ( ug ae dea Nex we ca eay oe ha ao a ea above ca be exeded o he roduc cae For exae ug Berga reroducg forua we dcued ea above aey he Pf = f equao by each varabe earaey we r w e he reroducg forua for A ( ace o roduc doa f a Berga ere we u -roduc of oe deoa ere (ee he ae dea [4] [5] for uch er cae of he u d ad he u oyd Th e obervao cruca for he roof of he heore of h oe aey for our har heore o race roduc of Sege doa of he ecod ye Beow we ree a ebeddg for aayc Berga ye ace o roduc of Sege doa of he ecod ye a oe ore acao of roducve dea we dcued The udy of hee ew aayc ace fro varou o a ereg ad earae robe Lea We have he foowg eae ρ f( z z b ( z z dv( z dv( z = α f ( z z b ( z z dv( z dv( z ; = +α where ( ;ρ = = The roof foow fro eae above ad he equay f = f f ( ad eae of +α ea 5 f( z cb ( z z f for z α f H( Noe for = cae h og eae ca be ee [] The foowg heore wa roved [] I erve a a bae for our roof Theore Le ad be fxed uber defed above Le ao r ad be wo vecor beogg o R Le > ad r > = ( d q Le ( ad ( The P a r bouded oeraor o L ( where + P f( ξ = C b ( ξ z ( b ( z z f( z dv( z ad ξ ay o fro I a bouded Berga roeco wh ove Berga ere for oe ove coa C Le u oe h heore ca be eay exeded (for = cae o he roduc of Sege doa of ecod ye foowg adard rocedure of addg varabe ad rear we dd above Th eco devoed o foruao ad roof of a a reu of h aer A revou cae of aayc fuco a u d oyd u ba ad uerhaface C + ad cae of ace of haroc fuco Eucdea ace [4] [7] [] [] [] he roe of he Berga rereeao forua cruca hee ue ad our roof are heavy baedo ad oe ea we rovded above ad hey are arae o cae we codered before [7] [] [8] The cruca roe ayg he exaded Berga roeco T h aer we away aue ha arge + eough ad a aura uber I ow a vara of Berga rereeao forua avaabe ao Berga-ye aayc fuco ace ubuar doa over yerc coe ad h ow fac (ee [3] cruca ao varou race robe aayc fuco ace ubuar doa (ee [3] ad varou referece here I ao ued a our roof beow We ar fro A cae where > or = hoogeeou Sege doa of he ecod ye he ur o ace ay Sege doa of A he ecod ye Noe he fr ar of our heore he fac ha he Sege doa hoogeeou eea Theore Le f A ( where = or > R > = for oe fxed arge eough deedg o araeer of Sege doa ad The f ( z z A ( where = = ( + Probe of Phyc Maheac ad Techc (3 5 87

7 RF Shaoya SM Kureo wh reaed eae for or Ad he revere ao rue For each fuco g A ( here a fuco F A ( uch ha F( z z = g( z for a Le addo 88 = z ( Tf( z z = C fw ( b(( z w dv( w =+ = where C a Berga coa Le ao > for oe fxed arge eough ove uber deedg o araeer of Sege doa The he T Berga-ye egra oeraor (exaded Berga roeco acg a a bouded oeraor fro A ( o A ( where = ( for a > = where аarge eough uber deedg o araeer of Sege doa ad The roof of heore urg he roof of heore varou rerco o aear h rerco ca be reoved f we coder A ( ace where = ( ad for a > = where а arge eough uber deedg o araeer of Sege doa ad We foow he roof of he u ba cae (ee [] ad acuay reea argue fro here for h geera cae ug reare of he revou eco Fr we how he ecod ar of h heore Le T [ f( z z ] = = C f( w b ( z w dv( w = = ( + ; z = ; arge eough The ( Tf ( z z = f( z ; z f A ; < q by ea 4 We how ha T ac fro ( A o ( A f arge eough Th fhe he roof of oe ar our heore For h we ue ea 3 For T we have egra oeraor (exaded Berga roecor Fr we have ug Hoder equay wce ad ea 3 for γ +γ = ; + = ; where γ > axa ; γ +τ > axa ; τ> ax B B = A = ( d q = = f ( w b ( z w dv ( w C( I J = = γ = C f( w b ( z w dv ( w = γ b ( z w dv ( w z = = γ J C f( w b ( z w dv ( w = τ C b ( z z z = ; = for τ = ( γ ; ow he foowg eae ( dv z C f Проблемы физики математики и техники (3 5 ad hece we have ( Tf( z z ( b ( z z ( b ( z z = z = x + y = z The a eae aga foow drecy fro equay of ea 3 ad Fub heore ad oe cacuao baed o eae +τ +τ [ b ( z z ][ b ( z z ] A γ v b z w dv z C3 b w w w = = ( ( [ ( ] The coe eco of codo o araeer baed o eeea cacuao eay how ha uch γ ad γ ca be choe f ad are arge eough The roof of oe ar of heore ow coee To how he fr aero of heore for = or ( earaey we refer he reader o [] where arae argue he u ba baed o eae for Berga ere ca be ee Noe h cae we u coder aoher Berga ye oeraor oeraor foowg aga he roof of he u ba cae Le f A ( < We coder = cae refryg for > o he u ba cae Le ( Tf ( z z = = c f( w w = b ( z w dv ( w dv ( w

8 О a race oeraor Berga ye aayc ace Sege doa of he ecod ye = + > = where arge eough Pu = z = The we have by our z ea o egra rereeao ( Tf ( z = f( z z z Noe for = ow eough o egrae boh de by Sege doa ad he ay Lea 4 (a we dd he u ba We have he ( Tf c f ; where = ( + Sce = A ( A ( b ( z w dv( z = ( + ( b ( z w b( z z dv( z = for oe c b( w w ; w = = + Le > ow We aga foow u ba cae Le γ + α + = = = = γ = ( Tg ( z = ( b( z z g( w α = ( bww ( b ( z wdvw ( = γ α = deedg o The ( Tg a for < q< q ad for oe fxed vaue of γ q α = A ( o q A ( a wa how above Nex fx * ( αγ o ha T = ( ad ow (ee q [6] ( A T = A for ( q + = where q ( = d Thu ( T a ( A ( o ( A ( for a ( q Thu he roof of heore fhed Ideed u ( Tg( w = g( z z = + b ( z w dv ( z dv ( z = ( Tg + ( z = ( b( z z f ( w = + ( = b ( z w b( w w dv( w = + > > = Theore 3 foow drecy fro Berga reroducg forua rovded he revou eco for A ace ad oe eeeary eae e Hoder equay for fuco We rovde deaed roof Theore 3 Le f A ( R > for oe arge eough ove The f ( z z A ( where = Ad he re- = vere ao rue For each fuco g A ( here a fuco F A ( uch ha F( z z = g( z Le addo = ( Tf( z z = C f( w b( z wdv ( w = + z = Le ao > for oe fxed arge eough ove The he T Berga-ye egra oeraor (exaded Berga roeco a bouded oeraor acg fro A ( o A ( = ( > = = for a arge eough Proof of heore 3 τ Noe ug he obvou roery of b ( z z fuco we have oe ar of he heore ce we have obvouy ha τ u f( z z [ b ( z z] z u u f( z z [ b ( z z ] z z τ τ [ b ( z z ];τ ++τ = ττ > τ = Le u how he revere cao for h heore For h we have o ue wo aero whch we foruaed above aey ea 3 ad rooo Fr we have ha f f A ( ; = = ad f ( Tf ( z z = = C f( w b ( z w dv( w = = + ;> z = he ( Tf ( z z = f( z z by rooo for a > arge eough z = The we have ha by Hoder equay for fuco ad Lea 3 ( Tf( z z [ b ( z z b ( z z] Probe of Phyc Maheac ad Techc (3 5 89

9 RF Shaoya SM Kureo C f ( ( ( A b z w dv w b z z = = C f ( ( ( A b z w dv w b z z = = + + C b ( w w b ( z w dudv = b ( z z f < A = for a > ad > w = Hece we have = ( Tf( z z b ( z z C f z = A The roof of heore 3 coee ow REFERENCES Beoe Reroducg roere ad L eae for Berga roeco Sege doa of ye II / Beoe ATKagou // Suda Mah 995 Vo 5 3 P 9 39 Kagou AT oa de Sege de ye II oyau de Berga Thee de docorae de 3 ee cyce / AT Kagou Yaoude Gd S Aay hoogeeou doa / S Gd // Rua Mah Survey 964 Vo 9 4 P 89 4 Shaoya F Toc he heory of A α ace / FShaoya A rbaha Teuber Texe zur Maheac Lezg Rud W Fuco heory oyd / W Rud New-Yor Acadec re Shaoya R O exrea robe wo Sege doa / R Shaoya // ROMAI Joura Vo 8 P Jevc M A oe o dagoa ag heore ace of aayc fuco he oyd / M Jevc M Pavovc R Shaoya // Pub Mah ebreche 9 Vo 74 / P 4 8 Shaoya R O exrea robe aayc Berga ye ace ubuar doa over yerc coe / R Shaoya S Kureo // Iue of Aay 4 Vo 3 P Shaoya R O a ew ace of aayc fuco oyba / R Shaoya O Mhc // Paee Joura 4 P 3 6 Shaoya R O race of hooorhc fuco o he u oyba / R Shaoya O Mhc // A Aa cree Maheac 9 3 P 98 Re G The dagoa ag heore xed or ace / G Re J Sh // Suda Mah 4 Vo 63 P 3 7 Car Rerco of H fuco he oyd / Car // Aerca Joura of Maheac 988 P Shaoya R Shar heore o race Berga ye ace ubuar doa over yerc coe / R Shaoya E Povr // Joura of Sbera Federa Uvery 3 Vo 6 4 P Shaoya R Mufucoa aayc ace roduc of bouded rcy eudocovex doa ad ebeddg heore / R Shaoya E Povr // Kraguevac Maheaca Joura 3 Vo 37 P 44 5 Chag S-Y Soe rece deveoe Fourer aay ad H heory o roduc doa / S-Y Chag R Feffera // Bue Aer Mah Socey 985 Vo P 43 6 Kagou A The dua of Berga ace Sege doa of ecod ye / A Kagou // IMHO- TEP 997 Vo P Areovc M O dace eae ad aoc decooo o ace of aayc fuco o rcy eudocovex doa / M Areovc R Shaoya // Bue Korea Maheaca Socey 4 Vo P Shaoya R O race of Q ye ace ad xed or aayc ace oyba / R Shaoya O Mhc // Sauau Maheaca Sear Vo 3 5 P 9 9 Beoe Moecuar decooo ad eroao / Beoe A Kagou // Iegra Equao ad Oeraor heory 998 Vo 3 P 5 77 Jb T Ieroao afod for roduc of rcy eudocoevx doa / T Jb A Saa // Coex Varabe P 34 Jaobcza P The boudary reguary of he ouo of he df equao roduc of rcy eudocovex doa / P Jaobcza // Pacfc Joura of Maheac 986 Vo P Areovc M O ebeddg race ad uer haroc fuco ace / M Areovc R Shaoya // Kraguevac Mah Joura 3 Vo 37 P Th wor wa uored by he Rua Foudao for Bac Reearch (gra ad by he Mry of Educao ad Scece of he Rua Federao (gra 744K Поступила в редакцию 65 9 Проблемы физики математики и техники (3 5