Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV
The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of s
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Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV Magnetic Schrödinger Operator 2
Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV
Victor Ivrii
Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV Magnetic Schrödinger Operator 2
123
Victor Ivrii Department of Mathematics University of Toronto Toronto, ON, Canada
ISBN 978-3-030-30544-4 ISBN 978-3-030-30545-1 https://doi.org/10.1007/978-3-030-30545-1
(eBook)
Mathematics Subject Classification (2010): 35P20, 35S05, 35S30, 81V70 © Springer Nature Switzerland AG 2019 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, expressed 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. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface The Problem of the Spectral Asymptotics, in particular the problem of the Asymptotic Distribution of the Eigenvalues, is one of the central problems in the Spectral Theory of Partial Differential Operators; moreover, it is very important for the General Theory of Partial Differential Operators. I started working in this domain in 1979 after R. Seeley [1] justified a remainder estimate of the same order as the then hypothetical second term for the Laplacian in domains with boundary, and M. Shubin and B. M. Levitan suggested me to try to prove Weyl’s conjecture. During the past almost 40 years I have not left the topic, although I had such intentions in 1985, when the methods I invented seemed to fail to provide the further progress and only a couple of not very exciting problems remained to be solved. However, at that time I made the step toward local semiclassical spectral asymptotics and rescaling, and new much wider horizons opened. So I can say that this book is the result of 40 years of work in the Theory of Spectral Asymptotics and related domains of Microlocal Analysi
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