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Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis the Helge Holden Anniversary Volume

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Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis the Helge Holden Anniversary Volume Nils Henrik Risebro and Kristian Seip, Editors Nils Henrik Risebro and Kristian Seip, Lyubarskii, Yurii Jakobsen, Espen R. Harald Hanche-Olsen, Gesztesy, Fritz Analysis and Stochastic Physics, Mathematical Equations, Differential Non-Linear Partial Series of Congress Reports Series of Congress Reports Non-Linear Partial Differential Non-Linear Partial Equations, Mathematical Physics, and Stochastic Analysis Differential Equations, The Helge Holden Anniversary Volume Mathematical Physics, Fritz Gesztesy, Harald Hanche-Olsen, Espen R. Jakobsen, Yurii Lyubarskii, Nils Henrik Risebro and Kristian Seip, and Stochastic Analysis Editors The Helge Holden Anniversary Volume This volume is dedicated to Helge Holden on the occasion of his 60th anniversary. It collects contributions by numerous scientists with expertise in non-linear partial differential equations (PDEs), mathematical physics, and stochastic analysis, reflecting to a large degree Helge Holden’s longstanding research interests. Fritz Gesztesy Accordingly, the problems addressed in the contributions deal with a large range of topics, including, in particular, infinite-dimensional analysis, linear and nonlinear Harald Hanche-Olsen PDEs, stochastic analysis, spectral theory, completely integrable systems, random matrix theory, and chaotic dynamics and sestina poetry. They represent to some extent the lectures presented at the conference Non-linear PDEs, Mathematical Physics and Espen R. Jakobsen Stochastic Analysis, held at NTNU, Trondheim, July 4–7, 2016. Yurii Lyubarskii The mathematical tools involved draw from a wide variety of techniques in functional analysis, operator theory, and probability theory. Nils Henrik Risebro This collection of research papers will be of interest to any active scientist working in Kristian Seip one of the above mentioned areas. Editors ISBN 978-3-03719-186-6 www.ems-ph.org SCR Gesztesy et al. | Egyptienne F | Pantone 116, 287 | RB 33 mm EMS Series of Congress Reports EMS Congress Reports publishes volumes originating from conferences or seminars focusing on any field of pure or applied mathematics. The individual volumes include an introduction into their subject and review of the contributions in this context. Articles are required to undergo a refereeing process and are accepted only if they contain a survey or significant results not published elsewhere in the literature. Previously published: Trends in Representation Theory of Algebras and Related Topics, Andrzej Skowron´ski (ed.) K-Theory and Noncommutative Geometry, Guillermo Cortiñas et al. (eds.) Classification of Algebraic Varieties, Carel Faber, Gerard van der Geer and Eduard Looijenga (eds.) Surveys in Stochastic Processes, Jochen Blath, Peter Imkeller and Sylvie Rœlly (eds.) Representations of Algebras and Related Topics, Andrzej Skowron´ski and Kunio Yamagata (eds.) Contributions to Algebraic Geometry. Impanga Lecture Notes, Piotr Pragacz (ed.) Geometry and Arithmetic, Carel Faber, Gavril Farkas and Robin de Jong (eds.) Derived Categories in Algebraic Geometry. Toyko 2011, Yujiro Kawamata (ed.) Advances in Representation Theory of Algebras, David J. Benson, Henning Krause and Andrzej Skowron´ski (eds.) Valuation Theory in Interaction, Antonio Campillo, Franz-Viktor Kuhlmann and Bernard Teissier (eds.) Representation Theory – Current Trends and Perspectives, Henning Krause, Peter Littelmann, Gunter Malle, Karl-Hermann Neeb and Christoph Schweigert (eds.) Functional Analysis and Operator Theory for Quantum Physics. The Pavel Exner Anniversary Volume, Jaroslav Dittrich, Hynek Kovarˇík and Ari Laptev (eds.) Schubert Varieties, Equivariant Cohomology and Characteristic Classes, Jarosław Buczyn´ski, Mateusz Michałek and Elisa Postinghel (eds.) Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis The Helge Holden Anniversary Volume Fritz Gesztesy Harald Hanche-Olsen Espen R. Jakobsen Yurii Lyubarskii Nils Henrik Risebro Kristian Seip Editors Editors: Fritz Gesztesy Harald Hanche-Olsen Department of Mathematics Espen R. Jakobsen Baylor University Yurii Lyubarskii Sid Richardson 305I, One Bear Place #97328 Kristian Seip Waco, TX 76798-7328 Department of Mathematical Sciences USA Norwegian University of Science and Technology Email: [email protected] Alfred Getz vei 1 7491 Trondheim Nils Henrik Risebro Norway Department of Mathematics Email: [email protected] University of Oslo [email protected] P.O. Box 1036, Blindern [email protected] N-0316 Oslo [email protected] Norway Email: [email protected] 2010 Mathematics Subject Classification: Primary: 15B52, 35J10, 35L65, 35Q41, 35Q51, 35Q53, 37K10, 42B20, 46N20, 46N30, 46T12, 47B36, 47F05, 60H20, 68N30, 76S05; secondary: 33C45, 35A01, 35A02, 35L80, 37D45, 39A12, 47A10, 47N20, 47N30, 60B20. Key words: Infinite-dimensional analysis, partial differential equations, hyperbolic conservation laws, stochastic analysis, spectral theory, discrete evolution, completely integrable systems, random matrix theory, chaotic dynamics. ISBN 978-3-03719-186-6 The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © European Mathematical Society 2018 Contact address: European Mathematical Society Publishing House Seminar for Applied Mathematics ETH-Zentrum SEW A21 CH-8092 Zürich, Switzerland Phone: +41 (0)44 632 34 36 Email: [email protected] Homepage: www.ems-ph.org Typeset by the editors using the authors’ TeX files: Harald Hanche-Olsen, Trondheim, Norway Printing and binding: Beltz Bad Langensalza GmbH, Bad Langensalza, Germany ∞ Printed on acid free paper 9 8 7 6 5 4 3 2 1 Preface This Festschrift is dedicated to Helge Holden on the occasion of his 60th birthday. Helge Holden was born to parents Finn Holden (1928–), a textbook author, histo- rian, and high school teacher, and Kirsten nee Wolfhagen (1931–1999), a librarian and psychologist, on September 28, 1956, in Oslo, Norway. Helge grew up with two younger brothers, Steinar, who is professor of economics at the University of Oslo, and Lars, who is Managing Director at the Norwegian Computing Center in Oslo. Interestingly, Helge has a joint paper [58]1 with his two brothers. Helge decided early to study mathematics and physics, and after serving the mandatory one year military service, he entered the University of Oslo in 1976. In the fall of 1980 he started to work on his cand.real. thesis with the late Prof. Raphael Høegh-Krohn (1938–1988) as advisor, working on solvable models in non-relativistic quantum mechanics. In the fall of 1981 he graduated with the cand.real. exam, his grades being so impressive that the result was reported to the King of Norway in the Council of State. Raphael Høegh-Krohn – a charismatic and brilliant mathematical physicist at the University of Oslo – brought Helge in contact with the group around Prof. Sergio Albeverio in Bochum, and the young mathematicians Fabio Martinelli, Werner Kirsch, and, Fritz Gesztesy. Fritz came to Oslo because he had found an improvement in an important paper by Raphael and Sergio (marking the beginning of an intensive collaboration with both of them), and at that occasion Fritz and Helge also started working together, and have continued to do so ever since. In those days, the work centered around so-called point interaction models in nonrelativistic quantum mechanics, and resulted in the book β[1], published by Springer in 1988, translated into Russian, and re-issued in a 2nd edition by the American Mathematical Society with an appendix by Prof. Pavel Exner in 2005. It has established itself as the standard reference in the field, and it is frequently cited in both the physics and mathematics literature. In the early 1980s, Norway was going through rapid and dramatic development. At Christmas of 1969, the first oil was discovered in the North Sea – the Ekofisk field – still one of the largest in the North Sea. The question was how to take advantage 1Numbers refer to the complete list of publications. vi Preface of this to the benefit of Norwegian society. Fortunately, the government decided to build up national competency in Norway, resulting in a dramatic improvement in the standard of living in Norway. Those who visited Norway in the early ’80s and visit now, will see an extreme makeover in Norway – it simply is a different country now. In the early ’80s, the Norwegian oil companies Saga, Hydro, and Statoil needed scientists with a good background in the sciences and in mathematics, and the companies supported mathematical research. Raphael and Helge, together with Nils Henrik Risebro, Lars Holden, Tore Gimse, Kyrre and Frode Bratvedt, and Christian Buchholz, embarked on the project to develop a full scale petroleum reservoir simulator. The approach was based at first on lots of enthusiasm and, retrospectively, less on deep knowledge of reservoir simulation; it was also the start of a life-long collaboration between Helge and Nils Henrik. Unfortunately, Raphael suddenly passed away in 1988, and Helge took over as PhD advisor of Nils Henrik and Lars. The development of the reservoir
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