Operator Theory, Pseudo-Differential Equations, and Mathematical Physics: The Vladimir Rabinovich Anniversary Volume PDF
Preview Operator Theory, Pseudo-Differential Equations, and Mathematical Physics: The Vladimir Rabinovich Anniversary Volume
Operator Theory Advances and Applications 228 Yuri I. Karlovich Luigi Rodino Bernd Silbermann Ilya M. Spitkovsky Editors Operator Theory, Pseudo-Differential Equations, and Mathematical Physics The Vladimir Rabinovich Anniversary Volume Operator Theory: Advances and Applications Volume 228 Founded in 1979 by Israel Gohberg Editors: Joseph A. Ball (Blacksburg, VA, USA) Harry Dym (Rehovot, Israel) Marinus A. Kaashoek (Amsterdam, The Netherlands) Heinz Langer (Vienna, Austria) Christiane Tretter (Bern, Switzerland) Associate Editors: Honorary and Advisory Editorial Board: Vadim Adamyan (Odessa, Ukraine) Lewis A. Coburn (Buffalo, NY, USA) Albrecht Böttcher (Chemnitz, Germany) Ciprian Foias (College Station, TX, USA) B. Malcolm Brown (Cardiff, UK) J.William Helton (San Diego, CA, USA) Raul Curto (Iowa, IA, USA) Thomas Kailath (Stanford, CA, USA) Fritz Gesztesy (Columbia, MO, USA) Peter Lancaster (Calgary, Canada) Pavel Kurasov (Lund, Sweden) Peter D. Lax (New York, NY, USA) Leonid E. Lerer (Haifa, Israel) Donald Sarason (Berkeley, CA, USA) Vern Paulsen (Houston, TX, USA) Bernd Silbermann (Chemnitz, Germany) Mihai Putinar (Santa Barbara, CA, USA) Harold Widom (Santa Cruz, CA, USA) Leiba Rodman (Williamsburg, VA, USA) Ilya M. Spitkovsky (Williamsburg, VA, USA) Yuri I. Karlovich Luigi Rodino Bernd Silbermann Ilya M. Spitkovsky Editors Operator Theory, Pseudo-Differential Equations, and Mathematical Physics The Vladimir Rabinovich Anniversary Volume Editors Yuri I. Karlovich Luigi Rodino Facultad de Ciencias Dipartimento di Matematica Universidad Autónoma del Estado de Morelos Università di Torino Cuernavaca, Morelos Torino Mexico Italy Bernd Silbermann Ilya M. Spitkovsky Fakultät für Mathematik Department of Mathematics Technische Universität Chemnitz College of William and Mary Chemnitz Williamsburg, VA Germany USA ISBN 978-3-0348-0536-0 ISBN 978-3-0348-0537-7 (eBook) DOI 10.1007/978-3-0348-0537-7 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2012951622 © Springer Basel 2013 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. Exempted from this legal reservation are brief excerpts in connection 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’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer Basel is part of Springer Science+Business Media (www.springer.com) Contents Preface .................................................................. vii S. Samko Vladimir Rabinovich: a Mathematician, Colleague and Friend ....... ix A. Antoniouk and N. Tarkhanov The Dirichlet Problem for the Heat Equation in Domains with Cuspidal Points on the Boundary .............................. 1 U. Battisti, T. Gramchev, L. Rodino and S. Pilipovi´c Globally Bisingular Elliptic Operators ............................... 21 A. B¨ottcher and A. Per¨al¨a The Index Formula of Douglas for Block Toeplitz Operators on the Bergman Space of the Ball ................................... 39 G. Burlak and V. Rabinovich The Green Function and Optical Field Enhancement in a Multilayered Microsphere with Metamaterial ................... 57 O. Chkadua, R. Duduchava and D. Kapanadze Potential Methods for Anisotropic Pseudo-Maxwell Equations in Screen Type Problems ........................................... 73 S. Dobrokhotov, D. Minenkov, V. Nazaikinskii and B. Tirozzi Functions of Noncommuting Operators in an Asymptotic Problem for a 2D Wave Equation with Variable Velocity and Localized Right-hand Side .................... 95 S. Grudsky and A. Rybkin On Toeplitz and Hankel Operators with Oscillatory Symbols Containing Blaschke Products and Applications to the KdV Equation ............................................... 127 N. Habal and B.-W. Schulze Mellin Quantisation in Corner Operators ............................ 151 vi Contents A.Yu. Karlovich and I.M. Spitkovsky Pseudodifferential Operators on Variable Lebesgue Spaces ........... 173 Yu.I. Karlovich and I. Loreto Hern´andez On Convolution Type Operators with Piecewise Slowly Oscillating Data .................................................... 185 V.V. Kravchenko and S.M. Torba Transmutations and Spectral Parameter Power Series in Eigenvalue Problems ............................................. 209 V.V. Kucherenko Estimate from Below for the Growth of Solution to the Navier-Stokes Equation When the Solution Blows Up ............... 239 A. Kufner, L.-E. Persson and N. Samko Some New Scales of Weight Characterizations of Hardy-type Inequalities .......................................... 261 G.M. N’Gu´er´ekata and A. Pankov Almost Periodic Elliptic Equations: Sub- and Super-solutions ....... 275 H. Rafeiro, N. Samko and S. Samko Morrey-CampanatoSpaces: an Overview ............................ 293 S. Roch Arveson Dichotomy and Essential Fractality ......................... 325 Y. Safarov Lower Bounds for the Counting Function of Integral Operators ...... 343 A. Sa´nchez-Nungaray and N. Vasilevski Toeplitz Operators on the Bergman Spaces with Pseudodifferential Defining Symbols ................................. 355 M. Seidel and B. Silbermann Finite Sections of Band-dominated Operators – Norms, Condition Numbers and Pseudospectra ...................... 375 F.-O. Speck On the Reduction of Linear Systems Related to Boundary Value Problems ........................................ 391 Preface This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) contains a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of Analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich’s research interests. Many of them are written by participants of the International workshop “Analysis, Operator The- ory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a longhistoryofscientificcollaborationwithVladimirRabinovich,andarepartially based on the talks presented there. The volume will be of great interest to researchersand graduate students in Differential Equations, Operator Theory, Functional and Harmonic Analysis. The Editors OperatorTheory: Advances andApplications,Vol.228,ix–xxv ⃝c 2013SpringerBasel Vladimir Rabinovich: a Mathematician, Colleague and Friend Stefan Samko Dedicated to the 70th anniversary of Professor Vladimir Rabinovich Itwasmypleasuretoaccepttheinvitationtowritethis introductorypapertothe volumededicatedtothe70thanniversaryofVladimirSamuilovichRabinovich,my university colleague in the “previous life” in the Soviet Union, collaborator and friend for more than 40 years. Vladimir Rabinovich, known to his friends and most of the colleagues as VolodyaRabinovich,wasborninKiev onSeptember 2, 1940,where his childhood passed.Inthe beginning ofthe Nazi invasionofUSSR in1941,whenmany people were evacuated from the Western regions to the interior parts of the country, his V. Rabinovich at his desk, M´exico City, May 2012.
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