Current Trends in Analysis and Its Applications: Proceedings of the 9th ISAAC Congress, Kraków 2013 PDF
Preview Current Trends in Analysis and Its Applications: Proceedings of the 9th ISAAC Congress, Kraków 2013
Trends in Mathematics Research Perspectives Vladimir V. Mityushev Michael V. Ruzhansky Editors Current Trends in Analysis and Its Applications Proceedings of the 9th ISAAC Congress, Kraków 2013 Trends in Mathematics ResearchPerspectives Research Perspectives collects core ideas and developments discussed at conferences and workshopsinmathematics,aswellastheirincreasinglyimportantapplicationstootherfields. Thissubseries’rapidpublicationofextendedabstracts,openproblemsandresultsofdiscus- sions ensures that readers are at the forefront of current research developments. Proposals forvolumescanbesubmittedusingtheonlinebookprojectsubmissionformatourwebsite www.birkhauser-science.com. Current Trends in Analysis and Its Applications Vladimir V. Mityushev Michael V. Ruzhansky Editors Proceedings of the 9th ISAAC Congress, Kraków 2013 Editors VladimirV.Mityushev MichaelV.Ruzhansky Dept.ofComputerSc.&Comp.Methods DepartmentofMathematics PedagogicalUniversity ImperialCollegeLondon Kraków,Poland London,UK ISSN2297-0215 ISSN2297-024X(electronic) TrendsinMathematics ISBN978-3-319-12576-3 ISBN978-3-319-12577-0(eBook) DOI10.1007/978-3-319-12577-0 LibraryofCongressControlNumber:2014958749 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 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. Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub- lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect tothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface The9thInternationalISAACCongresswasheldintheperiod5–9August2013in Krakow,Poland.ThemainorganiserwastheKrakowPedagogicalUniversity.The congress continued the successful series of biennial meetings previously held in USA (1997), Japan (1999), Germany (2001), Canada (2003), Italy (2005), Turkey (2007), UK (2009) and Russia (2011). The total number of participants of the congress was 502 coming from 62 countries, including the special guests and the OrganisingCommitteefromKrakowandRzeszow.Therewere12plenaryspeakers and 2 key speakers of the discussion group on applications. Totally, the congress had23sessionsspannedover4workingdays,while1daywasassignedtoexcur- sions.Thecongresswassponsoredbyindustrialpartners.Whenneeded,thePolish consulatesoverEuropeissuedfreevisasforparticipantsofthecongress. Oneofthemainfeaturesofthecongresswastheinvitationofindustrialspecial- ists, especially engineers working in industry, whose activity is related to applied mathematics(industrialmathematics)andcomputersciences.The9thInternational ISAAC Congress was an important scientific event during which mathematicians from different parts of the world had an opportunity to present new results and ideas.Itwasalsoagreatpossibilityforyoungmathematicianstocontactexpertsin avarietyoffields. TheatmosphereduringtheCongresswaswarmandfriendlyatthesessionsand atthesocialevents:banquet,excursions,footballmatchfollowedbyabarbeque.It is impossible to give the final score of the football match because too many goals werescored. The dates of the Congress, namely 5–9 August, provided for an extremely hot periodinthehistoryofKrakowthatcorrelatedwellwithhotandfruitfulscientific discussionsduringtheCongress. It is already a well-established tradition to award one or several outstanding young researchers during the ISAAC congress. The ISAAC award of the 9th In- ternationalISAACCongresswaspresentedto JassonVindas (UniversityofGhent,Belgium) v vi Preface for his outstanding results on the asymptotic behaviour of Schwartz distributions andtheirpointwisevalues. AttheISAACboardmeetingduringthecongressProfessorLuigiRodinoofthe UniversityofTurinwaselectedasthenewISAACPresident,andProfessorMichael Reissig of Freiberg University as the new Vice-President. The former president, Professor Michael Ruzhansky of Imperial College London, UK, has finished his 4-yearservice.Theelectionofthenewvice-presidentandnewrulesconcerningthe structureandfunctioningoftheinterestgroupswithinISAACcompletedthework onthenewISAACconstitutionthattookplaceintheyearbeforethecongress.The newconstitutionwasapprovedbythegeneralelectronicvotebyISAACmembers priortothecongress.FurtherinformationcanbefoundontheISAAChomepage www.mathisaac.org The ISAAC Board has decided the venue for the following 10th International ISAACCongressin2015tobetheUniversityofMacau. The plenary and key lectures given at the congress appear not here but in the independentvolume: Mityushev V., Ruzhansky M. (Eds.) Analytic Methods in Interdisciplinary Applications. SpringerProceedingsinMathematics&Statistics,Vol.116,Springer,2015. The present volume contains the texts of a selection of talks delivered at the congress.Asinthepreviousyears,someofthesessionsorinterestgroupsdecided to publish their own volumes of proceedings and are therefore excluded from the presentcollection.Theworkofthecongresswasspreadoverthefollowingsessions: • Complexvariablesandpotentialtheory, organisedbyT.Aliyev,A.Golberg,M.LanzadeCristoforis,S.Plaksa • DifferentialEquations:ComplexandFunctionalAnalyticMethods,Applications, organisedbyH.Begehr • Complex-analyticmethodsforappliedsciences, organisedbyS.V.Rogosin • CliffordandQuaternionAnalysis, organisedbyS.Bernstein,U.Kähler,I.SabadiniandF.Sommen • FixedPointTheoryandApplications, organisedbyE.Karapınar • SpacesofDifferentiableFunctionsofSeveralRealVariablesandApplications, organisedbyV.BurenkovandS.Samko • GeneralizedFunctions, organisedbyM.OberguggenbergerandS.Pilipovic´ • QualitativePropertiesofEvolutionModels, organisedbyK.Yagdjian,F.HirosawaandM.Reissig • NonlinearInfiniteDimensionalEvolutionsandControlTheorywithApplications, organisedbyI.Lasiecka,J.WebsterandG.Avalos • NonlinearPDE, organisedbyV.GeorgievandT.Ozawa • TopologicalandGeometricalMethodsofAnalysis, organisedbyA.Prykarpatskyi,Yu.ZelinskyiandK.Soltanov Preface vii • DidacticalApproachestoMathematicalThinking, organisedbyE.SwobodaandV.Mityushev • WaveletTheoryAnditsRelatedTopics, organisedbyK.FujitaandA.Morimoto • IntegralTransformsandReproducingKernels, organisedbyS.SaitohandJu.Rappoport • Pseudodifferentialoperators, organisedbyL.Rodino,J.ToftandM.W.Wong • MedicalMathematicsandComputing, organisedbyR.Gilbert,Ju.RappoportandV.Yakushev • ToeplitzOperatorsandTheirApplications, organisedbyS.GrudskyandN.Vasilevski • ApproximationTheoryandFourierAnalysis, organisedbyS.TikhonovandE.Liflyand • DifferentialandDifferenceEquationswithApplications, organisedbyL.Berezansky,J.Diblik,A.ZaferandM.Zima • AnalyticMethodsinComplexGeometry, organisedbyA.Schmitt • M-FrameConstructions, organisedbyK.Rudol,H.G.Stark,A.GrybosandD.Onchis • Applications of Queueing Theory in Modelling and Performance Evaluation of ComputerNetworks, organisedbyK.Grochla • AppliedMathematics, organisedbyS.Bosiakov • Otherscontainingothertalks, organisedbytheeditorsofthisvolume Wethanktheorganisersofallthesessionsofthecongressfortheirwork.They spent an enormous amount of time inviting participants, arranging their sessions, providing chairmen and creating a familiar and workshop-like atmosphere within their meetings. The session organisers were also responsible for collecting contri- butionstothisproceedingsvolumeandfortherefereeingprocessofthepapers. Krakow,Poland VladimirMityushev London,UK MichaelRuzhansky Contents PartI Tributes ATributetothe70thBirthdayofProfSaburouSaitoh . . . . . . . . . . 3 TsutomuMatsuura SergeiRogosin:AchievementssoFarandFurtherPlans . . . . . . . . . 5 MarynaDubatovskaya,AnnaKoroleva,andGennadyMishuris PartII DifferentialEquations:ComplexandFunctionalAnalytic Methods,Applications TheDegenerateSecond-OrderEllipticObliqueDerivativeProblem inaDomainwithaConicalBoundaryPoint . . . . . . . . . . . . . 11 MariuszBodziochandMikhailBorsuk OnLocallyDifferentiableSolutionsof the StationarySchrödinger EquationwithDiscontinuousCoefficients . . . . . . . . . . . . . . 19 K.N.Ospanov RiemannProblemsforSingle-PeriodicPolyanalyticFunctionsII . . . . 23 WangYufengandWangYanjin Riemann–HilbertProblemforMultiplyConnectedDomains . . . . . . 33 AnnaTytuła TheSchottky–KleinPrimeFunction . . . . . . . . . . . . . . . . . . . . 41 InezBadecka Green Function of the Dirichlet Problem for the Laplacian and Inhomogeneous Boundary Value Problems for the Poisson EquationinaPuncturedDomain . . . . . . . . . . . . . . . . . . . 49 BaltabekKanguzhinandNiyazTokmagambetov BoundaryValueProblemsandMethodofReflectionforQuarterRing andHalfHexagon . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 B.Shupeyeva ix x Contents HarmonicDirichletProbleminaRingSector . . . . . . . . . . . . . . . 67 YingWangandJinyuanDu TheParqueting-ReflectionPrinciple . . . . . . . . . . . . . . . . . . . . 77 HeinrichBegehr On Existence of the Resolvent and Discreteness of the Spectrum ofaClassofDifferentialOperatorsofHyperbolicType. . . . . . . 85 M.B.MuratbekovandM.M.Muratbekov OntheSingularitiesoftheEmden–FowlerTypeEquations . . . . . . . 93 RadosławAntoniKyciaandGalinaFilipuk Differential Equations with Degenerated Variable Operator attheDerivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 B.V.Loginov,Y.B.Rousak,andL.R.Kim-Tyan Cauchy Problem for a First Order Ordinary Differential System withVariableCoefficients . . . . . . . . . . . . . . . . . . . . . . . 109 A.Tungatarov General Solution of an n-th Order Linear Ordinary Differential EquationwithVariableCoefficients. . . . . . . . . . . . . . . . . . 117 A.TungatarovandB.Omarbayeva AboutaClassofTwoDimensionalVolterraTypeIntegralEquations withSingularBoundaryLines . . . . . . . . . . . . . . . . . . . . . 123 LutfyaRajabova OptimalControlProblemonOptimizationofResourcesProductivity . 133 AnastasiaA.UsovaandAlexanderM.Tarasyev PartIII SpacesofDifferentiableFunctionsofSeveralRealVariables andApplications TheAmalgamSpaces W(Lp(x),(cid:2){pn}) andBoundednessofHardy– LittlewoodMaximalOperators . . . . . . . . . . . . . . . . . . . . 145 A.TuranGürkanlı Spaces of Generalised Smoothness in Summability Problems forΦ-MeansofSpectralDecomposition . . . . . . . . . . . . . . . 163 TsegayeG.AyeleandMikhailL.Goldman Viewing the Steklov Eigenvalues of the Laplace Operator asCriticalNeumannEigenvalues . . . . . . . . . . . . . . . . . . . 171 PierDomenicoLambertiandLuigiProvenzano Generalized Fractional Integrals on Central Morrey Spaces and Generalizedσ-LipschitzSpaces . . . . . . . . . . . . . . . . . . . . 179 KatsuoMatsuoka PartIV QualitativePropertiesofEvolutionModels
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