The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the w
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Volodymyr Koshmanenko Mykola Dudkin Nataliia Koshmanenko
The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators
Operator Theory: Advances and Applications Volume 253 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 (Wien, Austria) Christiane Tretter (Bern, Switzerland) Associate Editors: Vadim Adamyan (Odessa, Ukraine) Wolfgang Arendt (Ulm, Germany) Albrecht Böttcher (Chemnitz, Germany) B. Malcolm Brown (Cardiff, UK) Raul Curto (Iowa, IA, USA) Fritz Gesztesy (Columbia, MO, USA) Pavel Kurasov (Stockholm, Sweden) Vern Paulsen (Houston, TX, USA) Mihai Putinar (Santa Barbara, CA, USA) Ilya M. Spitkovsky (Williamsburg, VA, USA)
Honorary and Advisory Editorial Board: Lewis A. Coburn (Buffalo, NY, USA) Ciprian Foias (College Station, TX, USA) J.William Helton (San Diego, CA, USA) Thomas Kailath (Stanford, CA, USA) Peter Lancaster (Calgary, Canada) Peter D. Lax (New York, NY, USA) Donald Sarason (Berkeley, CA, USA) Bernd Silbermann (Chemnitz, Germany) Harold Widom (Santa Cruz, CA, USA)
Subseries Linear Operators and Linear Systems Subseries editors: Daniel Alpay (Beer Sheva, Israel) Birgit Jacob (Wuppertal, Germany) André C.M. Ran (Amsterdam, The Netherlands) Subseries Advances in Partial Differential Equations Subseries editors: Bert-Wolfgang Schulze (Potsdam, Germany) Michael Demuth (Clausthal, Germany) Jerome A. Goldstein (Memphis, TN, USA) Nobuyuki Tose (Yokohama, Japan) Ingo Witt (Göttingen, Germany)
Volodymyr Koshmanenko • Mykola Dudkin
The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators
Volodymyr Koshmanenko Institute of Mathematics National Academy of Sciences of Ukraine Kyiv, Ukraine
Mykola Dudkin Kyiv Polytechnic Institute National Technical University of Ukraine Kyiv, Ukraine
Translated by Nataliia Koshmanenko
Original Ukrainian edition published by Institute of Mathematics, NAS of Ukraine, Kyiv, 2013 ISSN 0255-0156 ISSN 2296-4878 (electronic) Operator Theory: Advances and Applications ISBN 978-3-319-29533-6 ISBN 978-3-319-29535-0 (eBook) DOI 10.1007/978-3-319-29535-0 Library of Congress Control Number: 2016940830 Mathematics Subject Classification (2010): 47A10, 47A55, 28A80 © Springer International Publishing Switzerland 2016 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 regu
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