Springer Proceedings in Mathematics & Statistics Alexey Karapetyants Vladislav Kravchenko Elijah Liflyand Editors Modern Methods in Operator Theory and Harmonic Analysis OTHA 2018, Rostov-on-Don, Russia, April 22–27 Selected, Revised and Extended Contributions Springer Proceedings in Mathematics & Statistics Volume 291 Springer Proceedings in Mathematics & Statistics This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including operation research and optimization. In addition to an overall evaluation of the interest, 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 mathematical and statistical research today. More information about this series at http://www.springer.com/series/10533 Alexey Karapetyants Vladislav Kravchenko (cid:129) (cid:129) fl Elijah Li yand Editors Modern Methods in Operator Theory and Harmonic Analysis OTHA 2018, Rostov-on-Don, Russia, – April 22 27 Selected, Revised and Extended Contributions 123 Editors Alexey Karapetyants Vladislav Kravchenko Institute of Mathematics, Mechanicand Department ofMathematics Computer Sciences andRegional Cinvestav Mathematical Center SantiagodeQuerétaro, Querétaro,Mexico SouthernFederal University Rostov-on-Don, Russia Elijah Liflyand Department ofMathematics Bar-Ilan University Ramat Gan,Israel ISSN 2194-1009 ISSN 2194-1017 (electronic) SpringerProceedings in Mathematics& Statistics ISBN978-3-030-26747-6 ISBN978-3-030-26748-3 (eBook) https://doi.org/10.1007/978-3-030-26748-3 MathematicsSubjectClassification(2010): 47Bxx,46Exx,35Qxx,42-xx,46E15,46E30,46E35,42-00 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This volume assembles new results concerning the methods, problems, and appli- cationsofoperatortheoryandharmonicanalysis.Presentedbyleadingresearchers, chaptersnotablytouchonrecentdevelopmentsinspectraltheory,withapplications toPDEsandreal-worldproblems,alongwithadeepemphasisonthenewtrendsin operator theory and function spaces theory, such as variable exponent spaces and objectsofvariablenature.Thepublishedresultswillmainlyattractresearcherswho are interested in real and complex variable methods, applications to PDEs, and explorationofnewthemesandtrendsinharmonicanalysisandoperatortheory.The relevance of the topics covered in this volume, is stipulated, in particular, by the study of complicated multiparameter objects that require the involvement of operators with variable parameters and functional spaces with fractional and even variable exponents. ThisvolumeconsistsmainlyoftheworksofspeakersattheannualInternational Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications (OTHA-2018), which took place on April 22–27, 2018, at the Southern Federal University in Rostov-on-Don, Russia. Information on this and preceding conferences is available at the conference website http://otha.sfedu.ru/. Every year numerous investigators from research and educational institutions worldwide participate in OTHA conferences. Among them are mathematicians from Russia, China, the United States, the United Kingdom, Israel, Finland, Germany, Canada, Italy, Spain, Portugal, Sweden, Mexico, Colombia, Armenia, Azerbaijan, Jordan, Iran, UAE, Belarus, Kazakhstan, Poland, Lithuania, Uzbekistan, and Lithuania. One of the main features of OTHA conferences is the existenceofaveryspecialcreativeatmosphere.Thisresultsfrombothopportunities to form numerous contacts and collaborations and the sharing of inspirational presentations and ideas. The conference in 2018 was supported by the Regional Mathematical Center of the Southern Federal University in collaboration with the InstituteofMathematics,MechanicsandComputerScienceoftheSouthernFederal University.ItwasalsosupportedbyagrantfromtheRussianFoundationforBasic v vi Preface Research(https://www.rfbr.ru/)andbytheInternationalSocietyforAnalysisandits Applications (ISAAC, isaacmath.org). Wealsonotethatthisvolumeispreparedaspartofaspecialagreementbetween theISAACsocietyandSpringer.WethanktheISAACsocietyforitsmanyyearsof fruitfulcollaborationandsupport,andwethankSpringerforprovidingsuchagreat opportunity. We thank all the authors of this volume for their participation and contributions. Weexpressourimmenseregretatthelossoftwoparticipants(plenaryspeakers) who frequently presented at OTHA conferences, our dear friends and great math- ematicians,StasysRutkauskas(Lithuania)andGarnikKarapetyan(Armenia),both passing in 2018. We have reserved several pages of this volume to honor the memory of these great researchers and friends. Rostov-on-Don, Russia Alexey Karapetyants Santiago de Querétaro, Mexico Vladislav Kravchenko Ramat Gan, Israel Elijah Liflyand Professor Garnik Karapetyan – (1958/02/03 2018/11/29) WithkindpermissionofHeghinePetrosyan.Copyrightremainswiththeauthor Professor Garnik Karapetyan, an outstanding mathematician, a specialist in dif- ferentialequationsanddifferentiablefunctionsofseveralvariablesandotherrelated areas, and a Distinguished Professor of the Russian–Armenian University (RAU), passed away on November 29, 2018. The diverse scientific activity of Prof. G. Karapetyan meant that he was well-knowninthemathematicalcommunity.Oneofthemainpartsofthetheoryof differential equations and functional analysis, the general theory of differential equationsinthespacesofdifferentiablefunctions,isassociatedwithhisname.His researchplayedasignificantroleinthedevelopmentofageneraltheoryofintegral representations and embedding theorems in multianisotropic functional spaces. ProfessorGarnikKarapetyanwasbornonFebruary3,1958,inLeninakan(now Gyumri),ArmenianSSR.In1975,hestartedundergraduatestudiesattheFacultyof MechanicsandMathematicsofYerevanStateUniversity(YSU)andgraduatedcum laudein1980.In1983hedefendedhisPh.D.thesisandstartedworkasanassistant attheDepartmentofNumericalAnalysisoftheFacultyofInformaticsandApplied Mathematics at YSU. From 1990 to 1994, he held the position of dean of the vii viii ProfessorGarnikKarapetyan(1958/02/03–2018/11/29) Faculty of Informatics and Applied Mathematics at YSU. He was head of the Mathematics Olympiad Committee of Armenia for 2 years starting in 1997. In 2002, he founded the Department of Mathematics and Mathematical Modeling at RAU.In2007,hesuccessfullydefendedhisD.Sc.thesisentitled“Propertiesofthe solutionsofregularhypoellipticequations.”In2008,hereceivedtheacademicrank of professor from the Higher Attestation Commission of the Republic of Armenia and the title of Distinguished Professor at RAU. In 2008, he became a member of the Scientific Council of RAU and the Dissertation Council in Mathematics of the Republic of Armenia. From 2015, he was director of the Applied Mathematics and Informatics program at RAU. He was the first director of the InstituteofMathematicsandInformaticsatRAU.ProfessorGarnikKarapetyanwas awardedtheMedalofAnaniaShirakatsi,bydecreeofthePresidentoftheRepublic of Armenia. Formanyyears,hewasco-headofthescientificseminar“Functionalspacesand their applications in mathematical physics,” first at YSU and then RAU. He authored and co-authored 8 textbooks and manuals and more than 60 research articles. His research was mainly devoted to elliptic and hypoelliptic differential equations, the study of the properties of functions in different multianisotropic spaces, and the integral representations and embedding theorems for functions in multianisotropic spaces. Thesizelimitation appliedtothistextmakesitpossibletoonlybrieflydescribe someof,butnotall,thestudiesheconducted,oftenwithstudents,whichresultedin significant advances and a new deep understanding. His main research activity encompassed: (cid:129) The convergence of Galerkin approximations to the solution of the Dirichlet problem for different classes of hypoelliptic equations. (cid:129) Liouville and Phragmén–Lindelöf type theorems for general regular equations. (cid:129) The behavior of solutions of a certain class of hypoelliptic and l-elliptic equations in bounded and unbounded domains. (cid:129) Estimates for solutions of quasi-elliptic equations in Hölder spaces. (cid:129) Schauder-type estimates for solutions of semi-elliptic equations with variable coefficients. (cid:129) Thestudyofsolutionsofhypoellipticanddegenerateequationsinahalf-space. (cid:129) The study of boundary value problems for regular quasilinear equations in unbounded domains. (cid:129) Proof of stabilization of solutions for regular and hypoelliptic equations of different classes. (cid:129) The study of solutions of nondegenerate equations depending on a parameter. (cid:129) The study of eigenvalues of self-adjoint semi-elliptic operators. (cid:129) Proof of multiplicative inequalities of Gagliardo–Nirenberg type in multian- isotropic Sobolev spaces. (cid:129) Approximations of solutions of semi-elliptic equations in a half-space. (cid:129) Computation of the index of semi-elliptic operators. (cid:129) Proof of the Noetherianness of semi-elliptic and nondegenerate operators. ProfessorGarnikKarapetyan(1958/02/03–2018/11/29) ix (cid:129) Applicationofthesmallparametermethodfortheapproximationofeigenvalues of regular hypoelliptic operators. (cid:129) Integral representations of functions in different multianisotropic spaces and their embedding theorems. Professor Garnik Karapetyan was a highly qualified professional in his field and a talented leader. One of his distinguishing qualities was paying particular attention andrespecttopeopleandtheirproblems.Hewasimpeccablyhonestandprincipled inhisworkandtactfulinrelationships with hisfamilymembers, relatives,friends, colleagues,andstudents.Hewastremendouslycharismatic;heenjoyedexceptional trust and reverence from students. Not only did he demonstrate genuine interest in everything new in science and life in general, but he also triggered interest in his students and those surrounding him. Professor G. Karapetyan was not only well-known among scientists and aca- demics;thegeneralpublicalsoknewhimthankstotheeducationalprogram“Open Lesson,” broadcast on public TV in Armenia. Whatisparticularlysadforallhisfriendsandcolleaguesisthatheleftthisworld during his creative ascent. During his last 5–6 years he actively conducted fruitful research on the integral representations of functions in multianisotropic Sobolev spacesandtheembeddingtheoremsforsuchspaces.Hismostrecentwork,inthefield of isotropic or anisotropic Sobolev spaces, formed part of a body of work that included research by distinguished scientists including S. Sobolev, L. Schwartz, S. Nikolskii, S. Agmon, O. Besov, H. Triebel, E. Gagliardo, P. Lizorkin, I.Slobodetsky,I.Nechas,V.Burenkov,S.Uspenskii,V.Solonnikov,G.Demidenko, A.Kufner,andmanyothers. Most recently, Prof. G. Karapetyan obtained integral representations for func- tions in multianisotropic Sobolev spaces generated by regular Newton polyhedra, and, based on these representations, proved embedding theorems for such spaces. Some of the results he obtained are not yet published. His plans for future work included the description of traces of functions in multianisotropic spaces on hypersurfacesofdifferentdimensionsandtheoremsonthecontinuationoffunctions outsidetheirdomainofdefinition.Wehopethatthisworkwillbecontinuedbyhis disciples. Thefamily,relatives,friends,colleagues,andstudentsofGarnikKarapetyan,as well as Armenian mathematics, suffered an irretrievable loss due to his untimely death. Cherished memories of Garnik Karapetyan will forever remain in our hearts. Adamyan G. V., Aramyan R. H., Avetisyan P. S., Babayan A. H., Baghdasaryan A. G., Berberyan S. L., Darbinyan A. A., Darbinyan A. R., Gevorgyan G. G., Ghazaryan E. M., Ghazaryan H. G., Harutyunyan K. V., Harutyunyan T. N., Margaryan V. N., Petrosyan H. A., Sandoyan E. M., Sargsyan G. Z., Tonoyan R. N., and Tumanyan A. G.