Handbook of complex analysis. Geometric function theory

876 Pages·2005·5.31 MB·English

by  Reiner Kuhnau

HANDBOOK OF COMPLEX ANALYSIS
GEOMETRIC FUNCTION THEORY
This Page Intentionally Left Blank
HANDBOOK OF COMPLEX ANALYSIS
G F T
EOMETRIC UNCTION HEORY
Volume 2
Editedby
R. KÜHNAU
Martin-Luther-UniversitätHalle-Wittenberg
Halle(Saale),Germany
2005
Amsterdam •Boston • London • NewYork •Oxford•Paris
San Diego •San Francisco • Singapore •Sydney • Tokyo
ELSEVIERB.V. ELSEVIERInc. ELSEVIERLtd ELSEVIERLtd
SaraBurgerhartstraat25 525BStreet,Suite1900 TheBoulevard,LangfordLane 84TheobaldsRoad
P.O.Box211,1000AEAmsterdam SanDiego,CA92101-4495 Kidlington,OxfordOX51GB LondonWC1X8RR
TheNetherlands USA UK UK
©2005ElsevierB.V.Allrightsreserved.
ThisworkisprotectedundercopyrightbyElsevierB.V.,andthefollowingtermsandconditionsapplytoitsuse:
Photocopying
Singlephotocopiesofsinglechaptersmaybemadeforpersonaluseasallowedbynationalcopyrightlaws.PermissionofthePublisherand
paymentofafeeisrequiredforallotherphotocopying,includingmultipleorsystematiccopying,copyingforadvertisingorpromotional
purposes,resale,andallformsofdocumentdelivery.Specialratesareavailableforeducationalinstitutionsthatwishtomakephotocopiesfor
non-profiteducationalclassroomuse.
Permissions may be sought directly from Elsevier’s Rights Department in Oxford, UK; phone: [phone], fax: (+44)
1865 853333, e-mail: [email protected] may also be completed on-line via the Elsevier homepage (http://www.
elsevier.com/locate/permissions).
IntheUSA,usersmayclearpermissionsandmakepaymentsthroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,
MA01923,USA;phone:[phone],fax:[phone],andintheUKthroughtheCopyrightLicensingAgencyRapid
ClearanceService(CLARCS),90TottenhamCourtRoad,LondonW1P0LP,UK;phone:[phone];fax:[phone].
Othercountriesmayhavealocalreprographicrightsagencyforpayments.
DerivativeWorks
Tablesofcontentsmaybereproducedforinternalcirculation,butpermissionofthePublisherisrequiredforexternalresaleordistributionof
suchmaterial.PermissionofthePublisherisrequiredforallotherderivativeworks,includingcompilationsandtranslations.
ElectronicStorageorUsage
PermissionofthePublisherisrequiredtostoreoruseelectronicallyanymaterialcontainedinthiswork,includinganychapterorpartofa
chapter.
Exceptasoutlinedabove,nopartofthisworkmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,
electronic,mechanical,photocopying,recordingorotherwise,withoutpriorwrittenpermissionofthePublisher.
Addresspermissionsrequeststo:Elsevier’sRightsDepartment,atthefaxande-mailaddressesnotedabove.
Notice
NoresponsibilityisassumedbythePublisherforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligence
orotherwise,orfromanyuseoroperationofanymethods,products,instructionsorideascontainedinthematerialherein.Becauseofrapid
advancesinthemedicalsciences,inparticular,independentverificationofdiagnosesanddrugdosagesshouldbemade.
Firstedition2005
LibraryofCongressCataloginginPublicationData
AcatalogrecordisavailablefromtheLibraryofCongress.
BritishLibraryCataloguinginPublicationData
AcataloguerecordisavailablefromtheBritishLibrary.
ISBN:044451547x
ThepaperusedinthispublicationmeetstherequirementsofANSI/NISOZ39.48-1992(PermanenceofPaper).
PrintedinTheNetherlands
Preface
As is the case for Volume 1 of this Handbook, this is not a textbook but a collection
of independent survey articles about new developments in Geometric Function Theory.
Again,itwouldofcoursebeimpossibletocoveranextensivefieldlikethisonecompletely.
Nevertheless,Idonotdoubtthatitspublicationwillhelptomakethistheoryinterestingto
newpeopleandwillattractnewresearcherstosolvingitsproblems.
I amgratefulto ProfessorEdgarReich forhiskindadvicein connectionwithsomeof
thearticles.Imostgratefullyacknowledgethefriendlycooperationandexpertsupportof
Dr.A.SevensterandMrs.AndyDeelenfromElsevier.Lastbutnotleast,Ihavetothank
ZigmasKryžiusfromVTEXTypesettingservicefortheexcellentprinting.
ReinerKühnau
v
This Page Intentionally Left Blank
List of Contributors of Volume 1
Aksent’ev,L.A.,KazanStateUniversity,Kazan(Ch.7)
Andrievskii,V.V.,KentStateUniversity,Kent,OH(Ch.15)
Baernstein,A.II,WashingtonUniversity,St.Louis,MO(Ch.9)
Gardiner,F.P.,BrooklynCollege(CUNY),NewYork,NY (Ch.14)
Grinshpan,A.Z.,UniversityofSouthFlorida,Tampa,FL(Ch.10)
Hamilton,D.H.,UniversityofMaryland,CollegePark,MD(Chs.4–6)
Harvey,W.J.,King’sCollegeLondon,London(Ch.14)
Hayman,W.K.,ImperialCollegeofScience,TechnologyandMedicine,London(Ch.1)
Jenkins,J.A.,WashingtonUniversity,St.Louis,MO(Ch.13)
MacGregor,T.H.,UniversityofAlbany,Albany,NY (Ch.12)
Pommerenke,Ch.,TechnischeUniversitätBerlin,Berlin(Ch.2)
Prokhorov,D.V.,SaratovStateUniversity,Saratov(Ch.8)
Reich,E.,UniversityofMinnesota,Minneapolis,MN (Ch.3)
Shabalin,P.L.,KazanStateUniversity,Kazan(Ch.7)
Stephenson,K.,UniversityofTennessee,Knoxville,TN (Ch.11)
Wilken,D.R.,UniversityofAlbany,Albany,NY (Ch.12)
vii
This Page Intentionally Left Blank
List of Contributors
AndreianCazacu,C.,UniversityofBucharest,Bucuresti,Romania(Ch.17)
Bshouty,D.,DepartmentofMathematics,Technion,Haifa,Israel(Ch.10)
Dittmar, B., Martin-Luther-Universität Halle-Wittenberg, Halle an der Saale, Germany
(Ch.16)
Drasin,D.,PurdueUniversity,WestLafayette,IN(Ch.18)
Gehring,F.W.,UniversityofMichigan,AnnArbor,MI (Ch.1)
Gol’dberg,A.A.,Bar-IlanUniversity,RamatGan,Israel(Ch.18)
Hengartner,W.,UniversitéLaval,Québec,Canada(Ch.10)
Kirsch, S., Martin-Luther-Universität Halle-Wittenberg, Halle an der Saale, Germany
(Ch.6)
Krushkal,S.L.,Bar-IlanUniversity,RamatGan,Israel(Chs.2,5,11)
Kühnau, R., Martin-Luther-Universität Halle-Wittenberg, Halle an der Saale, Germany
(Chs.3,4,13,15,19)
Poggi-Corradini,P.,KansasStateUniversity,Manhattan,KS(Ch.18)
Qiu,S.-L.,HangzhouDianziUniversity,Hangzhou,P.R.China(Ch.14)
Schmieder,G.,UniversitätOldenburg,Oldenburg,Germany(Ch.8)
Srebro,U.,Technion–IsraelInstituteofTechnology,Haifa,Israel(Ch.12)
Suffridge,T.J.,UniversityofKentucky,Lexington,KY (Ch.7)
Vuorinen,M.,UniversityofTurku,Turku,Finland(Ch.14)
Wegmann,R.,Max-Planck-InstitutfürAstrophysik,Garching,Germany(Ch.9)
Yakubov,E.,HolonAcademicInstituteofTechnology,Holon,Israel(Ch.12)
ix