Special Functions, Partial Differential Equations, and Harmonic Analysis: In Honor of Calixto P. Calderón PDF
Preview Special Functions, Partial Differential Equations, and Harmonic Analysis: In Honor of Calixto P. Calderón
Springer Proceedings in Mathematics & Statistics Constantine Georgakis Alexander M. Stokolos Wilfredo Urbina E ditors Special Functions, Partial Diff erential Equations, and Harmonic Analysis In Honor of Calixto P. Calderón Springer Proceedings in Mathematics & Statistics Volume 108 Moreinformationaboutthisseriesathttp://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. Constantine Georgakis • Alexander M. Stokolos Wilfredo Urbina Editors Special Functions, Partial Differential Equations, and Harmonic Analysis In Honor of Calixto P. Calderón 123 Editors ConstantineGeorgakis AlexanderM.Stokolos DePaulUniversity GeorgiaSouthernUniversity Chicago,IL,USA Statesboro,GA,USA WilfredoUrbina RooseveltUniversity Chicago,IL,USA ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-3-319-10544-4 ISBN978-3-319-10545-1(eBook) DOI10.1007/978-3-319-10545-1 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014953383 MathematicsSubjectClassification(2010):01-06,01A65,42B25,44A10,42B05,42C10,46E35,35J70, 32A55,34H10,37N25,37N35,42B37,42B35,92B99,97M60 ©SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) CalixtoP.Calderón Inthebackrow(fromlefttoright):AlbertoP.Calderón(brother),MargaritaCalderón(sister), withherdaughterinarmsRaquelPeñayLillo(niece),MatildeGarcíaGallo(mother),Matilde Calderón(sister) Inthefrontrow(fromlefttoright):SilvestrePeñayLillo(brotherinlaw),SilvestrePeñay Lillo,Jr.(nephew),HaydeePeñayLillo(niece),MaríaTeresaCalderón(sister),Dr.Pedro Calderón(father)andCalixtoP.Calderón(himself). Preface Calixto P. Calderon, like many Argentine mathematicians of his generation, was introducedandmentoredintoHarmonicAnalysisandPartialDifferentialEquations attheUniversityofBuenosAiresbyAlbertoGonzalezDominguez,histeacherand Ph.D.advisor,whosementorwasDavidTamarkinofBrownUniversity.Moreover, CalixtoP.Calderonprovedveryearlyinhiscareertobeaninfluentialteacherand mentorforLuisA.Caffarelli,aworldauthorityonFreeBoundaryValueProblems inPartialDifferentialEquationsandrecentrecipientoftheprestigiousIsrael’sWolf Prize. Thepaperspresentedbyhisfriendsorcolleaguesandsomeofhisformerdoctoral studentsattheconferenceinhonorofCalixtoP.CalderonatRooseveltUniversity wereindicative toalargeextentofthewidescopeanddepthofhisresearchwork and scholarship in pure and applied mathematics. Furthermore, the friendly and festiveatmosphereamongtheparticipantsattheconferencefromtheUSAandLatin America reflected very much his wonderful charismatic personality and humility. A memorable moment was the scene where the president of Roosevelt University, while addressing the participants briefly, asked those in the audience who were Calixto P. Calderon’s students to raise their hands, and Luis A. Caffarelli’s hand wentup! CalixtoP.Calderon’snumerousresearchpublicationsinclude:ClassicalFourier series and Orthogonal Expansions, Calderon-Zygmund Theory of Singular Inte- grals, Ordinary and Partial Differential Equations especially the Navier–Stokes p.d.e,ProbabilityTheory,MathematicalModelsAppliedtoBiologyandMedicine, and History of Mathematics and Science. Clearly, his work in pure Mathematics wasinfluencedbyAlbertoGonzalezDominguez,AlbertoC.Calderon—hisbrother, Antoni Zygmund, and several other collaborators and colleagues. Whereas his considerableresearchworkinMathematicalBiologyandMedicinemighthavebeen theresultoftheinfluencehereceivedwhilegrowingupfromhisfather,Dr.PedroJ. Calderon,anaccomplishedphysiciantrainedinMedicineinBuenosAiresandParis. One can’t help but note that, likewise, the father of Aristotle, Nicomachus, who vii viii Preface didexperimentalresearchinBiologyandBotany,althoughhewasPlato’sgreatest studentofpurephilosophy,wasalsoamedicalphysicianand,infact,thepersonal physicianofKingPhilipofMacedon. ExceptfortheappointmentsattheUniversityofCuyo,theUniversityofBuenos Aires, and the University of Minnesota, Calixto P. Calderon spent most of his distinguished academic career at the University of Illinois at Chicago (U.I.C.). He taughtavarietyofcoursesrangingfromHarmonicAnalysisandPartialDifferential Equations to Probability Theory and Statistics, and had several Ph.D. students. His strong interest in probability and statistics may be attributed in part to his Statistics teacher—Roque Carranza at the University of Buenos Aires. He wrote two papers on the subject including a paper on Kolmogorov’s strong law of large numbers for pair-wise independent random variables. The themes of the thesis of hisPh.D.students,likehisresearch,rangedfromHarmonicAnalysistothehistory ofSpanishmathematicsandrelatedscience.DuringhistenureatU.I.C.,CalixtoP. Calderon was an active participant and invited speaker at seminars in the Chicago area, including the Calderon-Zygmund Seminar at the University of Chicago, and the analysis seminars at U.I.C., and at DePaul University. Furthermore, Calixto P. Calderonwasanexcellentandeloquentlecturer,andremainedactivelyengagedin issuesrelatedtomathematicseducationatU.I.C. Theeditorsofthisvolumeofchapterswouldliketothanktheorganizersofthe conferenceinhonorofCalixtoP.Calderonandtheauthorsofthecontributedpapers. Chicago,IL,USA ConstantineGeorgakis Statesboro,GA,USA AlexanderM.Stokolos Chicago,IL,USA WilfredoUrbina Contents RemembrancesandSilhouettes ................................................ 1 CalixtoP.Calderón TheCalderónBrothers,aHappyMathematicalRelation................... 7 AlexandraBellow CalixtoCalderónAsIKnewHim.............................................. 13 LuisCaffarelli AnAppraisalofCalixtoCalderón’sWorkinMathematicalBiology....... 15 EvansAfenya RemarksonVariousGeneralizedDerivatives ................................ 25 J.MarshallAsh SomeNonStandardApplicationsoftheLaplaceMethod................... 41 CalixtoP.CalderónandWilfredoO.Urbina FejérPolynomialsandChaos................................................... 49 DmitriyDmitrishin,AnnaKhamitova,andAlexanderM.Stokolos ANoteonWidder’sInequality ................................................. 77 ConstantineGeorgakis SolyanikEstimatesinHarmonicAnalysis..................................... 87 PaulHagelsteinandIoannisParissis SomeOpenProblemsRelatedtoGeneralizedFourierSeries............... 105 KazarosS.Kazarian ComputationalAnalysisforaMathematicalModeloftheMechanics ofAneurysmDevelopmentandRupture ...................................... 115 TorA.Kwembe ix
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