Analysis As a Life: to the 80Th Birthday of Professor H. Begehr

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Analysis as a Life Dedicated to Heinrich Begehr on the Occasion of his 80th Birthday Editors Sergei Rogosin Ahmet Okay Çelebi Department of Economics Mathematics Department Belarusian State University Yeditepe University Minsk, Belarus Ata¸sehir, Istanbul, Turkey

ISSN 2297-0215 ISSN 2297-024X (electronic) Trends in Mathematics ISBN 978-3-030-02649-3 ISBN 978-3-030-02650-9 (eBook) https://doi.org/10.1007/978-3-030-02650-9

Library of Congress Control Number: 2018967001

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This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface

The book contains several important research contributions from the different branches of analysis. These papers are combined due to the common idea. The authors express their gratitude to Professor Heinrich Begehr for his help in their research career and dedicate articles to Begehr’s 80th birthday. Scientiﬁc achievements by Prof. H. Begehr are well known (see a short biograph- ical paper below as well as the paper Vaitekhovich T.: Heinrich Begehr: Citation for his 70th birthday, Analysis, v. 30 (1), pp. 1–26). More important for analytic society is his numerous collaborations with people all around the world. Many mathematicians from different countries are thankful to him for the role he played in their scientiﬁc life. Professor H. Begehr is known also for his initiatives. Among them is his role in the creation and further development of the International Society for Analysis, its Applications and Computation (ISAAC). With this volume the colleagues and friends of Professor Heinrich Begehr would like to thank him and wish to have a long life in analysis.

Minsk, Belarus Sergei Rogosin Istanbul, Turkey Ahmet Okay Çelebi August 2018

v Analysis as a Life: To the 80th Birthday of Professor H. Begehr

Professor Heinrich Gottfried Werner Begehr has celebrated his 80th birthday a few months earlier than this book is appeared. We would like to present here a few biographic data and briefly describe his research career. Also we have given some reminiscence about his life. More information can be found at Prof. H.Begehr’s web-site at FU-Berlin: http://page.mi.fu-berlin.de/begehrh/. He was born in Halle/ Germany on April 17, 1939. He has obtained his M.Sc. degree in Freie Universtität (FU) Berlin in 1966. He has completed his Dr. rer. Nat. degree in 1968 under the supervision of Professor Alexander Dinghas and his habilitation in 1970 (just in 2 years) in FU Berlin. He worked as a Professor in FU from 1970 to 2004, that is, until the date he is retired. In 1972 he has been elected as the Director of I. Math. Inst. FU Berlin. He held this position with some interruptions, for about 18 years. In 1975 Professor R. P. Gilbert visited Hahn-Meitner Institute in Berlin by an Alexander von Humboldt award for a semester. During this period Professor Begehr and Professor Gilbert have interchanged many ideas. This cooperation have ended up with many joint papers, the book project “Transformations, Transmutations, and Kernel Functions” composed of two volumes, together with the first steps towards the foundation of the journal “Complex Analysis, Theory and Applications”. Later the name of this journal has evolved as “Complex Variables and Elliptic Equations”. The next important outcome of this cooperation was founding the “International Society for Analysis, its Applications and Computation (ISAAC)”. This society was founded in 1995. The sequence of International ISAAC Congress’s, which are held in every 2 years, has started in 1997 at the University of Delaware. He was the secretary and treasurer of newly founded ISAAC. In 2001, Professor Begehr was the first elected president of the Society. The other presidents were Man Wah Wong (2005–2009), Michael Ruzhansky (2009–2013), Luigi Rodino (2013–2017) and Michael Reissig (2017–). After 2005 he was secretary and treasurer until the elections in 2017. ISAAC has supported more than 35 conferences all around the world, besides 11 ISAAC Congresses. Begehr’s first book with title “Topics in complex analysis: Four lectures given at the University of Delaware in January and February 1977” has appeared in 1977.

vii viii Analysis as a Life: To the 80th Birthday of Professor H. Begehr

Now he has seven published books. He was one of the editors of 10 proceedings of the ISAAC congresses. He has translated or edited 30 books. He is the co-editor of – Berliner Studienreihe zur Mathematik, Heldermann Verlag, since 2004; (together with R. Gorenflo). – Series on Analysis, Applications and Computation, World Scientific, since 2005; (together with R. P. Gilbert, M. W. Wong). – Complex Variables and Elliptic Equations, Taylor and Francis, since 2008; (senior editor together with M. Lanza de Cristoforis and A. Pankov) He is also in the editorial board of the following journals and series of monographs: – Complex Variables and Elliptic Equations, since 1982; Taylor and Francis, – Monograph and Surveys in Pure and Applied Mathematics, since 1997; Chapman and Hall/CRC-Press, – Research Notes in Mathematics, since 1997; Chapman and Hall/CRC-Press, – International Society of Analysis, its Applications and Computation, during 1997–2004; Kluwer Academic publisher, – General Mathematics, since 2001; Lucian Blaga, Univ. of Sibiu, Romania, – Journal of Applied Functional Analysis, since 2004; NOVA Publ., – Journal of Analysis and Applications, since 2005; SAS Intern. Publ., – Advances in Algebra and Analysis, since 2005; Urmi Scientific Vision, – International Journal of Mathematics and Applications (IJMA), since 2005; Global Research Publications Serials, India – International Journal of Mathematics and Mathematical Sciences (IJMMS), since 2006; Hindawi Publ., – Advances in Pure and Applied Mathematics, since 2008; Hedermann Verlag, Lemgo.

He has been invited to many foreign universities as “Guest Professor” and “Guest Research Professor”. He is a member of the following academic societies: – Berlin Mathematical Society, since 1984; – International Society of Analysis, its Applications and Computation, since 1996; – Member of Russian Academy of Natural Sciences, Armenian Branch, since 2002; – Member of European Acad. Sci., since 2004; – Foreign Member of Russian Academy of Natural Sciences, since 2003; – Honorary Member of Europaische Akad. Naturwiss. in Hanover, since 2003. The number of his research papers are more than 180. He is a very productive Ph.D. adviser. He has advised at least 26 students from nine different countries. He was a devoted teacher and continued to hold the weekly seminars after his retirement, too. Lastly, tracing his research papers and books, anybody can observe that Heinrich Begehr is an excellent co-worker. Analysis as a Life: To the 80th Birthday of Professor H. Begehr ix

We are sure that his contributions to complex partial differential equations and generally to the world of Mathematics will continue through himself and his 26 students. Minsk, Belarus Sergei Rogosin Istanbul, Turkey Ahmet Okay Çelebi

Berlin 2001

Ankara in April 2004 x Analysis as a Life: To the 80th Birthday of Professor H. Begehr

Ankara 2007 Analysis as a Life: To the 80th Birthday of Professor H. Begehr xi

Ankara 2007

Moscow 2011 xii Analysis as a Life: To the 80th Birthday of Professor H. Begehr

Collage for Heinrich Begehr’s 70th birthday Analysis as a Life: To the 80th Birthday of Professor H. Begehr xiii

ISAAC 2009 in London

Krakow 2013 xiv Analysis as a Life: To the 80th Birthday of Professor H. Begehr

Krakow 2013

Macao 2015 Analysis as a Life: To the 80th Birthday of Professor H. Begehr xv

Heinrich Begehr and Okay Çelebi at the ISSAC 2017 in Växjö, Sweden

Jan Begehr xvi Analysis as a Life: To the 80th Birthday of Professor H. Begehr

Heinrich Begehr

Begehr in Yerevan in 2002 Analysis as a Life: To the 80th Birthday of Professor H. Begehr xvii

Catania 2005

Graz 1997 Few Stories from the Scientiﬁc Life of Professor Heinrich Begehr

Heinrich was visiting me at my beach house. The wind was very heavy as was the ocean. We decided to go swimming anyway. The water was too rough for me so I headed back to shore after a while. Heinrich continued to swim on. When I was on land the waves had gotten really rough and I started to worry about Heinrich. I became really worried that he might drown and did not know what to do. I could not see him because of the high waves. Some sailors came to shore and I asked had they seen someone swimming; they said yes he was still swimming out to sea. Eventually, when I had given up hope, Heinrich steps out of the sea. It seems he had wanted to swim to one of the control lights, which is a good swim in calm water but unbelievable in the rough sea we were experiencing now. Newark, DE, USA Robert Gilbert

I hope all is ﬁne and well in Berlin, or wherever your travels have happened to take you at the moment. It saddens me to realize it must already be 12 years since we met last—on the conference in Shantou, China, where I remember that unhappy baywatch when he realized that he cannot stop you from swimming about 1 km further out than permitted! Prague, Czech Republic Miroslav Englis

I would like to recall a very important phase in our relationship with Heinrich, which represents him not only as a great scientist, but a high-quality person. In 1991 Heinrich together with the world’s best mathematicians arrived in Tbilisi for the symposium dedicated to the 100th anniversary of Niko Muskhelishvili. This was the time of high fulﬁllment for Georgia: we declared independence, elected our ﬁrst president, set on to building the free, democratic society. The guests met with the president and returned home impressed with the encounter. At home they were hosted by Giorgi Manjavidze, I have wonderful memories of these days... Sadly, Georgia had to face some hard times soon after that, legitimately appointed president was overthrown by the communist junta, a period of real hardship was

xix xx Few Stories from the Scientific Lifeof Professor Heinrich Begehr underway. This period lasted long, nothing positive could be seen on the horizon. When Heinrich learned that our family was also experiencing difficulties, and shy to offer direct help to my father, he came up with an idea to support us in a very delicate way: an offer to the young people in the Complex Analysis group, to form a scholarship team. This was the first scientific scholarship possibility in Georgia. I will never forget how caring Heinrich was towards our group and especially to me, after my father’s death. Without his corrections and advice, it would have been impossible for us to publish articles or to participate in conferences and congresses. He empowered us to lead my father’s way and the traditions of Complex Analysis that had rich history in Georgia. Tbilisi, Georgia Nino Manjavidze

This story happened in winter 2001 at the Conference AMADE in Minsk. It is well- known that Heinrich Begehr prefers the sport style of life, practically does not drink alcohol. At AMADE-2001 we organized an excursion to Khatyn’, the memorial complex dedicated to villages burned by fascists together with people lived in these villages. The complex was built in the following manner: an empty well and a bell are built on the place of each burned house of the Khatyn’ village. Winter 2001 in Minsk was fairly cold and snowy. In these circumstances the bells sounded especially eerie and impressive. When participants of the Conference returned to the bus, there was rather long silence. Then Heinrich said “give me a glass of vodka...” For him as a German it was even harder than for all others. Minsk, Belarus Sergei Rogosin

When I was working on my PHD with Professor Haack at the TU-Berlin, I was interested in getting the book on Potential Theory by Josip Plemelj which was in the library of Professor A. Dinghas at the Free University Berlin. Professor Dinghas was a not simple person and usually did not lend any of his books in particular to some guy from the TU. He was always in the center of a cloud of lady students. However, Heinrich Begehr was also one of the students of Dinghas. So, I asked him for help and indeed Heinrich could get Plemelj’s book and within very few days I copied the whole book which till this day is one of the juwels in my library. The book is wonderful and helped me signiﬁcantly for my thesis. Till this day I am grateful to Heinrich Begehr.

Stuttgart, Germany Wolfgang Wendland Contents

Deformation of Complex Structures and Boundary Value Problem with Shift ...... 1 G. Akhalaia, G. Giorgadze, G. Makatsaria, and N. Manjavidze Dirichlet Problem for Poisson and Bi-Poisson Equations in Clifford Analysis ...... 19 Ümit Aksoy Boundary Eigenvalues of Pluriharmonic Functions for the Third Boundary Condition on the Unit Polydiscs...... 39 Alip Mohammed Survey of Some General Properties of Meromorphic Functions in a Given Domain ...... 47 G. Barsegian Boundary Value Problems in Polydomains...... 69 Ahmet Okay Çelebi Completeness Theorems on the Boundary in Thermoelasticity ...... 93 Alberto Cialdea A Circle Pattern Algorithm via Combinatorial Ricci Flows...... 117 Dong-Meng Xi, Shi-Yi Lan, and Dao-Qing Dai Strong Asymptotic Analysis of OLPs on the Unit Circle by Riemann-Hilbert Approach ...... 139 Yufeng Wang, Yifeng Lu, and Jinyuan Du Time Dependent Solutions for the Biot Equations ...... 171 Robert P. Gilbert and George C. Hsiao Schwartz-Type Boundary Value Problems for Monogenic Functions in a Biharmonic Algebra ...... 193 S. V. Gryshchuk and S. A. Plaksa

xxi xxii Contents

The String Equation for Some Rational Functions...... 213 Björn Gustafsson Newtonian and Single Layer Potentials for the Stokes System with L∞ Coefﬁcients and the Exterior Dirichlet Problem...... 237 Mirela Kohr, Sergey E. Mikhailov, and Wolfgang L. Wendland Special Functions Method for Fractional Analysis and Fractional Modeling ...... 261 S. V. Rogosin and M. V. Dubatovskaya On Elliptic Systems of Two Equations on the Plane...... 279 A. P. Soldatov Real Variable Inverse Laplace Transform...... 303 Vu Kim Tuan, A. Boumenir, and Dinh Thanh Duc