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Mats Andersson Jan Boman Christer Kiselman Pavel Kurasov Ragnar Sigurdsson Editors Analysis Meets Geometry The Mikael Passare Memorial Volume
Editors Mats Andersson Department of Mathematics Chalmers University of Technology Göteborg, Sweden Christer Kiselman Department of Information Technology Uppsala University Uppsala, Sweden Jan Boman Department of Mathematics Stockholm University Stockholm, Sweden Pavel Kurasov Department of Mathematics Stockholm University Stockholm, Sweden Ragnar Sigurdsson Science Institute University of Iceland Reykjavik, Iceland ISSN 2297-0215 Trends in Mathematics ISBN 978-3-319-52469-6 DOI 10.1007/978-3-319-52471-9 ISSN 2297-024X (electronic) ISBN 978-3-319-52471-9 (ebook) Library of Congress Control Number: 2017951453 Mathematics Subject Classification (2010): 01-00, 32-XX, 51-XX, 35-XX Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part 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 or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents Preface... vii Part I: Memorial Contributions Mikael Passare: Curriculum Vitae... 3 Mikael Passare spublications... 5 List of Visited Countries... 11 G. Passare My Life with Mikael... 15 C. O. Kiselman Mikael Passare (1959 2011)......................................... 35 M. Carlehed Mikael Passare... 59 Part II: Research Articles M. Nisse and M. Passare Amoebas and Coamoebas of Linear Spaces... 63 M. Andersson, H. Samuelsson Kalm, E. Wulcan, and A. Yger One Parameter Regularizations of Products of Residue Currents.... 81 M. Andersson and E. Wulcan On the Effective Membership Problem for Polynomial Ideals........ 91 R. J. Berman On the Optimal Regularity of Weak Geodesics in the Space of Metrics on a Polarized Manifold... 111 B. Berndtsson A Comparison Principle for Bergman Kernels... 121 Z. B locki Suita Conjecture from the One-dimensional Viewpoint.............. 127 J. Boman Siciak s Theorem on Separate Analyticity... 135
vi Contents J.-P. Calvi Mikael Passare, a Jaunt in Approximation Theory... 147 T. de Wolff Amoebas and their Tropicalizations a Survey... 157 J. Forsgård Coamoebas of Polynomials Supported on Circuits................... 191 D. Quang Hai and P. J. Thomas Limit of Green Functions and Ideals, the Case of Four Poles......... 213 J. Hoppe Geodesics on Ellipsoids............................................. 229 I. Itenberg, V. Kharlamov, and E. Shustin Welschinger Invariants Revisited... 239 P. Johansson Some Results on Amoebas and Coamoebas of Affine Spaces......... 261 C. O. Kiselman and S. Samieinia Convexity of Marginal Functions in the Discrete Case... 287 L. Lempert Modules of Square Integrable Holomorphic Germs... 311 J. Lundqvist An Effective Uniform Artin Rees Lemma... 335 G. Mikhalkin Amoebas of Half-dimensional Varieties... 349 A. Rashkovskii A log Canonical Threshold Test... 361 B. Shapiro and A. Solynin Root-counting Measures of Jacobi Polynomials and Topological Types and Critical Geodesics of Related Quadratic Differentials..... 369 J. Sjöstrand and M. Vogel Interior Eigenvalue Density of Jordan Matrices with Random Perturbations... 439
Preface Dear Reader, This volume is dedicated to the life and work of Mikael Passare, who unexpectedly passed away in September 2011 at the age of 52. It will give you a chance to study several texts that are inspired by his mathematical interests either directly so, or in a more indirect way. One chapter is even coauthored by Mikael. We are indeed happy that so many outstanding scientists have answered our call to contribute a chapter to the book. Before arriving to these mathematical chapters, you can get an idea about Mikael s life and his far-reaching research, which spans from analysis in several complex variables and complex geometry to amoebas and tropical geometry. We hope that you will enjoy getting acquainted with the ideas of a great mathematician and a great human being. Mats Andersson Jan Boman Christer Kiselman Pavel Kurasov Ragnar Sigurdsson
Mikael Passare 1959 2011