Analysis of Operators on Function Spaces: The Serguei Shimorin Memorial Volume PDF
Preview Analysis of Operators on Function Spaces: The Serguei Shimorin Memorial Volume
Trends in Mathematics Alexandru Aleman Haakan Hedenmalm Dmitry Khavinson Mihai Putinar Editors Analysis of Operators on Function Spaces The Serguei Shimorin Memorial Volume Trends in Mathematics TrendsinMathematicsisaseriesdevotedtothepublicationofvolumesarisingfrom conferences and lecture series focusing on a particular topic from any area of mathematics.Itsaimistomakecurrentdevelopmentsavailabletothecommunityas rapidlyaspossiblewithoutcompromisetoqualityandtoarchivetheseforreference. ProposalsforvolumescanbesubmittedusingtheOnlineBookProjectSubmission Formatourwebsitewww.birkhauser-science.com. Materialsubmittedforpublicationmustbescreenedandpreparedasfollows: Allcontributionsshouldundergoareviewingprocesssimilartothatcarriedoutby journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, shouldberejected.Highqualitysurveypapers,however,arewelcome. We expecttheorganizerstodelivermanuscriptsina formthatisessentiallyready fordirectreproduction.AnyversionofTEX isacceptable,buttheentirecollection of files must be in one particular dialect of TEX and unified according to simple instructionsavailablefromBirkhäuser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essentialthatthefinalversionoftheentirematerialbesubmittednolaterthanone yearaftertheconference. Moreinformationaboutthisseriesathttp://www.springer.com/series/4961 Alexandru Aleman • Haakan Hedenmalm • Dmitry Khavinson • Mihai Putinar Editors Analysis of Operators on Function Spaces The Serguei Shimorin Memorial Volume Editors AlexandruAleman HaakanHedenmalm MathematicsDepartment DepartmentofMathematics LundUniversity TheRoyalInstituteofTechnology Lund,Sweden Stockholm,Sweden DmitryKhavinson MihaiPutinar DepartmentofMathematics MathematicsDepartment UniversityofSouthCalifornia UniversityofCalifornia Tampa,FL,USA SantaBarbara,CA,USA ISSN2297-0215 ISSN2297-024X (electronic) TrendsinMathematics ISBN978-3-030-14639-9 ISBN978-3-030-14640-5 (eBook) https://doi.org/10.1007/978-3-030-14640-5 MathematicsSubjectClassification(2010):30-XX,32-XX,46-XX,47-XX,12-XX,31-XX ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered companySpringerNatureSwitzerlandAG. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This book is dedicated to Serguei Shimorin, eminent mathematician and virtuoso lensman. Serguei’smathematicswasforgedatoneofthepreeminenthubsofmathematical analysisofthetwentiethcentury:St.PetersburgUniversityandtheSteklovInstitute of Mathematics at St. Petersburg. He carried over countries and generations the preciouslegacyofHavinandNikolski’slegendaryseminar.Thechoicesofresearch topics he made, well represented by the articles contained in the present volume, are the product of years of accumulated skills and quiet introspection. Serguei’s vastmathematicalculture,especiallyinFunctionTheoryandFunctionalAnalysis, isheldinhighesteembyhiscolleaguesandcollaborators. Shimorin was a man of few words, written or spoken. He sought beauty in simplicity, uncontaminated by the tumult of modern life. For those close to him, including probably his many undergraduate students at the Royal Institute of TechnologyatStockholm,heemanatedpurelight—alasting,invaluableheritage. Serguei’smathematicalgiftwascomplementedbyartistic dispositions.He was adevoutclassicalmusicconcertgoer(especiallyonthelavishSt.Petersburgscene) andan accomplishedpianist.Hisreligiousadmirationfornaturetookmanyforms andinparticularhedistilledtheserenityandmysteryoflandscapeintophotos.They speakbythemselvesaboutthemanwecelebrateandmourninthisvolume: http://www.photosight.ru/users/119352/ Somereminiscencesfromtheeditors: Alexandru Aleman: Serguei was a dear friend. I admired his mathematical work before knowing him and am truly grateful for the beautiful subtle ideas he exchangedwithme. Dmitry Khavinson: For me personally he has always represented (by now almost non-existent) legendary Russian, St. Petersburg ‘intelligentsia’, always firmlyguidedinlifebyformidable,non-bendingmoralhumanisticprinciples. v vi Preface Mihai Putinar: On the occasion of his visit to Singapore, where we had ample professional, social and cultural activities, he was obstinate in declining our company to discover the city. He wanted to experience alone the wonders of the luxuriant vegetation, unique architecture and human variety. For Serguei the freshnessofdiscoverywasprimordial. SergueiissurvivedbyhiswifeOlgaMuzhdaba(geographer),daughterAnastasia Shimorina(linguist)andsonMikhailShimorin(musician). We thank Dorothy Mazlum and the team at Birkhäuser Verlag for making possiblethisbookproject. Lund,Sweden AlexandruAleman Stockholm,Sweden HaakanHedenmalm Tampa,FL,USA DmitryKhavinson SantaBarbara,CA,USA MihaiPutinar SergueiShimorin(1965–2016) Contents MyRecollectionsofSergueiShimorin......................................... 1 HaakanHedenmalm LocalizationofZerosinCauchy–deBrangesSpaces......................... 5 EvgenyAbakumov,AntonBaranov,andYuriiBelov RadiallyWeightedBesovSpacesandthePickProperty..................... 29 AlexandruAleman,MichaelHartz,JohnE.McCarthy,andStefanRichter InterpolationBetweenHilbertSpaces......................................... 63 YacinAmeur APanoramaofPositivity.I:DimensionFree ................................. 117 AlexanderBelton,DominiqueGuillot,ApoorvaKhare,andMihaiPutinar InnerFunctionsinReproducingKernelSpaces.............................. 167 RaymondCheng,JavadMashreghi,andWilliamT.Ross SphericallyQuasinormalPairsofCommutingOperators .................. 213 RaúlE.CurtoandJasangYoon RemarksontheInterplayBetweenAlgebraandPDE....................... 239 DmitryKhavinson WhichQuarticPolynomialsHaveaHyperbolicAntiderivative?........... 247 RajeshPereira PositiveIntegralKernelsforPolarDerivatives............................... 251 MihaiPutinarandSergueiShimorin TheWeakTypeEstimatesofTwoDifferentMartingaleTransforms Coincide........................................................................... 259 AlexanderReznikovandAlexanderVolberg PhotographsbySergueiShimorin ............................................. 275 vii My Recollections of Serguei Shimorin HaakanHedenmalm Abstract TheauthorshareshispersonalreminiscencesofSergueiShimorin. Keyword Shimorintheorem MSCCodes: 01A70 Serguei Shimorin died July 18, 2016, as the result of a hiking accident in the mountainsofAbkhazia,adisputedpartofGeorgiaintheCaucasus.Hewashiking withtwofriends,AndreiandRoman(whowerebrothers),andhewasabouttheto pioneerthecrossingofthecreekDzhampal.Unfortunatelytheattemptendedreally tragically. He was a young man, born in 1965 in Leningrad. His death is a major loss for Mathematicsand Swedish Mathematicsin particular. I would now like to sharesomeofmyrecollectionsconcerningSergueiandhisscientificachievements inMathematics,atLundUniversityandlateratKTH. In the fallsemester of 1990I visited Leningradthroughanacademicexchange program,involvingKVA(RoyalSwedishAcademyofSciences)andtheAcademy ofSciencesoftheUSSR.Iobtainedanominalstipendinrapidlydevaluingroubles, but,moreimportantly,Iwassuppliedwithafreehotelroomduringmyvisit.While inLeningrad,IencounteredseveralprominentparticipantsoftheAnalysisSeminar at LOMI (nowadaysPOMI), the Steklov Institute located at Fontanka27. Among thesewereNikolaiNikolski,NikolaiMakarov,VladimirPeller,AlexeiAlexandrov, to mention a few. This was a difficult time in the USSR, and the country fell apart just a year later. But there was nothing wrong with the hospitality, and I rememberbeinginvitedhometobothPellerandNikolski.Ataroundthistimethe factorizationmethodsinvolvingextremalfunctionsinBergmanspaceshadalready beendevelopedbymyselfaswellasothers(IwasinfluencedbyBorisKorenblum fromSUNYAlbany)andImadeacoupleofpresentationsonthistopicduringthe fallsemester.Ididnotnoticeitthen,butlaterIunderstoodthatamongtheattentive H.Hedenmalm((cid:2)) TheRoyalInstituteofTechnology,DepartmentofMathematics,Stockholm,Sweden e-mail:[email protected];https://people.kth.se/~haakanh/engindex.html ©SpringerNatureSwitzerlandAG2019 1 A.Alemanetal.(eds.),AnalysisofOperatorsonFunctionSpaces, TrendsinMathematics,https://doi.org/10.1007/978-3-030-14640-5_1 2 H.Hedenmalm listenerswasashyyoungmanbythenameofSergueiShimorin.Hewasstudying with Stanislav A. Vinogradov, who himself had studied with Victor P. Havin in 1968 in Leningrad. Apparently my presentationsmade an impression on Serguei, as a bit later he sent me a preprintentitled “Factorization of analytic functionsin weighted Bergman spaces” which subsequently appeared in Algebra i Analiz and inEnglishtranslationinSt.PetersburgMath.J.in1994.Thiswork(presumablya partofSerguei’s1993thesis)washighlyoriginal,especiallyasheinventedakind ofpseudodifferentialoperators(cid:2) suchthattheanalogofGreen’sformula α (cid:2) (cid:2) (h (cid:2) h −h (cid:2) h )dA = (h ∂ h −h ∂ h )ds 2 α 1 1 α 2 α 2 n 1 1 n 2 D ∂D would hold for an interval in α, where dA (z) = (1 −|z|2)αdA(z) is weighted α areameasure.Lateronhedevelopedthetheoryofthese(cid:2) furtherandcomputed α arelatedweightedbiharmonicGreenfunctionandobtaineditspositivity.Theissue whetherbiharmonicGreenfunctionsarepositiveisadelicatemattergoingbackto workofBoggioandHadamardfromaround1900.Anotherfascinatingcontribution is “Single-point extremal functions in weighted Bergman spaces”, where Serguei developedanewideaconnectingbetweenunivalenceanddivisorpropertiesofone- pointdivisors(analogsofBlaschkefactors). At some pointaround1994–1995I was invitedto the home ofSergueiand his family (wife Olga and children Anastasia and Mikhail) and I recall that I asked whether he had taken part in any kind of Math Olympiad. That kind of almost sportyactivitywasencouragedintheUSSRandapparentlySergueihaddonewellin somelocalsucholympiad,andshowedmeadiploma.Healsomentionedassuming programmingworkrightafterthe1987diplomabeforeenteringthePhDprogram. In 1996 I was taking part in a conference in Trondheim organizedby Kristian Seip. There I spoke with Alexander Borichev, with whom I had collaborated successfullywhenhewasa“forskarassistent”inUppsalainthe1990s.Hehadthen leftSwedenforFranceandnowthatIhadmovedtoLundfromUppsala,Isuggested hemightcometoLund.Hedeclined,butsuggestedIcouldbeinterestedinSerguei whom he found an excellent mathematician. With this strong recommendation Shimorinwashiredas“forskarassistent”inLundaround1998withanNFRgrant, afterspendingayearatUniversitédeBordeaux.ThelectureshipwhichImentioned toattractBorichevwentinsteadtoAlexandruAleman. IgotSergueiinterestedintheprojecttoshowthatthebiharmonicGreenfunction was positive for a general weight which was reproducing for a point and also logarithmicallysubharmonic.This was conjectured,but proveddifficultto obtain. Intheendwesucceeded,andSergueihadfundamentalinsighttowardthesolution. HederivedapropertyofthecorrespondingBergmankernelwhichtogetherwitha twiceappliedHele–Shawflowledtotheconjecturedpositivity.Alsointheworkon Hele–ShawflowonhyperbolicsurfacesSergueisuppliedkeyinsight.Hewasalways meticulously careful and sought elegantargumentswhenever possible. As a spin- off he produced the impressive paper “Wold-type decompositions and wandering subspacesforoperatorsclose to isometries”publishedby Crelle in 2001.Another
The list of books you might like
