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Friedrich Haslinger - D-bar Neumann Problem and Schrodinger Operators

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Friedrich Haslinger D-bar Neumann Problem and Schrodinger Operators

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The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted toBergman spaces of holomorphic d-bar functions in one and several complex variables.These operators are Hankel operators of special type. In the following the general complex is investigated ond-bar spaces over bounded pseudoconvex domains and on weightedd-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator.The last part contains a detailed account of the application of the methods to Schrdinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.

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Table of Contents Bibliography 1 R A Adams and J J F Fournier - photo 1
Table of Contents

Bibliography
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  • [27] K. Gansberger, Compactness of the Picture 12 -Neumann operator, Dissertation, University of Vienna, 2009.
  • [28] K. Gansberger and F. Haslinger, Compactness estimates for the Picture 13 - Neumann problem in weighted L 2 - spaces, Complex Analysis (P. Ebenfelt, N. Hungerbhler, J.J. Kohn, N. Mok, E.J. Straube, eds.), Trends in Mathematics, Birkhuser (2010), 159-174.
  • [29] F. Haslinger, The canonical solution operator to Picture 14 restricted to Bergman spaces, Proc. Amer. Math. Soc.129 (2001), 33213329.
  • [30] F. Haslinger, The canonical solution operator to Picture 15 restricted to spaces of entire functions, Ann. Fac. Sci. Toulouse Math. 11 (2002), 5770.
  • [31] F. Haslinger, Schrdinger operators with magnetic fields and the Picture 16 -equation, J. Math. Kyoto Univ. 46 (2006), 249-257.
  • [32] F. Haslinger, The Picture 17 -Neunmann operator and commutators between multiplication operators and the Bergman projection, Czechoslovakian J. of Math. (2008), 1247-1256.
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  • [41] B. Helffer and J. Sjstrand, Puits multiples en limite semi-classique IV- Etude du complex de Witten, Comm. Partial Differential Equations (1985), 245-340.
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