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Spectral Theory and Differential Operators
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  • Cited by 152
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Abbas, Tawfik Brown, Madelyne M. Ramasami, Allison and Zeytuncu, Yunus E. 2019. Spectrum of the Kohn Laplacian on the Rossi sphere. Involve, a Journal of Mathematics, Vol. 12, Issue. 1, p. 125.

    Ben-Artzi, Matania and Katriel, Guy 2019. Spline functions, the biharmonic operator and approximate eigenvalues. Numerische Mathematik,

    Trapani, Camillo Triolo, Salvatore and Tschinke, Francesco 2019. Distribution Frames and Bases. Journal of Fourier Analysis and Applications,

    Kovařík, Hynek and Mugnolo, Delio 2018. Heat Kernel Estimates for Schrödinger Operators on Exterior Domains with Robin Boundary Conditions. Potential Analysis, Vol. 48, Issue. 2, p. 159.

    Metafune, G. Negro, L. and Spina, C. 2018. Sharp kernel estimates for elliptic operators with second-order discontinuous coefficients. Journal of Evolution Equations, Vol. 18, Issue. 2, p. 467.

    Boulton, Lyonell Schroers, Bernd J. and Smedley-Williams, Kim 2018. Quantum Bound States in Yang–Mills–Higgs Theory. Communications in Mathematical Physics, Vol. 363, Issue. 1, p. 261.

    Bagarello, F. Inoue, H. and Trapani, C. 2018. Biorthogonal vectors, sesquilinear forms, and some physical operators. Journal of Mathematical Physics, Vol. 59, Issue. 3, p. 033506.

    Latos, Evangelos Morita, Yoshihisa and Suzuki, Takashi 2018. Stability and Spectral Comparison of a Reaction–Diffusion System with Mass Conservation. Journal of Dynamics and Differential Equations, Vol. 30, Issue. 2, p. 823.

    Bonforte, Matteo Figalli, Alessio and Vázquez, Juan Luis 2018. Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains. Analysis & PDE, Vol. 11, Issue. 4, p. 945.

    Beretta, Elena Francini, Elisa and Vessella, Sergio 2018. A transmission problem on a polygonal partition: regularity and shape differentiability. Applicable Analysis, p. 1.

    Lopes, A. O. and Thieullen, Ph. 2018. Modeling, Dynamics, Optimization and Bioeconomics III. Vol. 224, Issue. , p. 247.

    Ben-Artzi, Matania Croisille, Jean-Pierre Fishelov, Dalia and Katzir, Ron 2018. Discrete fourth-order Sturm–Liouville problems. IMA Journal of Numerical Analysis, Vol. 38, Issue. 3, p. 1485.

    Basti, Giulia Cacciapuoti, Claudio Finco, Domenico and Teta, Alessandro 2018. The three-body problem in dimension one: From short-range to contact interactions. Journal of Mathematical Physics, Vol. 59, Issue. 7, p. 072104.

    Graham, Cole Shean Lim, Tau Ma, Andrew and Weber, David 2018. Existence and non-existence of transition fronts in mixed ignition-monostable media. Nonlinearity, Vol. 31, Issue. 2, p. 651.

    Golénia, Sylvain and Mandich, Marc-Adrien 2018. Propagation Estimates for One Commutator Regularity. Integral Equations and Operator Theory, Vol. 90, Issue. 4,

    Dietlein, Adrian 2018. Full Szegő-Type Trace Asymptotics for Ergodic Operators on Large Boxes. Communications in Mathematical Physics, Vol. 362, Issue. 3, p. 983.

    Hislop, Peter D and Marx, Christoph A 2018. Dependence of the Density of States on the Probability Distribution for Discrete Random Schrödinger Operators. International Mathematics Research Notices,

    Hsiao, Chin-Yu and Marinescu, George 2017. Berezin–Toeplitz quantization for lower energy forms. Communications in Partial Differential Equations, Vol. 42, Issue. 6, p. 895.

    Lin, Fanghua 2017. Extremum problems of Laplacian eigenvalues and generalized Polya conjecture. Chinese Annals of Mathematics, Series B, Vol. 38, Issue. 2, p. 497.

    Prodan, Emil 2017. A Computational Non-commutative Geometry Program for Disordered Topological Insulators. Vol. 23, Issue. , p. 25.


Book description

This book is an introduction to the theory of partial differential operators. It assumes that the reader has a knowledge of introductory functional analysis, up to the spectral theorem for bounded linear operators on Banach spaces. However, it describes the theory of Fourier transforms and distributions as far as is needed to analyse the spectrum of any constant coefficient partial differential operator. A completely new proof of the spectral theorem for unbounded self-adjoint operators is followed by its application to a variety of second-order elliptic differential operators, from those with discrete spectrum to Schrödinger operators acting on L2(RN). The book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on the subject.


‘ … a new approach to the spectral theorem for self-adjoint unbounded operators … For readers with standard background in functional analysis and bounded operator theory the book can serve as a missing link to the more advanced literature.’

Source: Monatshefte für Mathematik

‘ … a concise and nicely written introduction to many important areas of this vast mathematical discipline … This short book (180 pages) will be very useful both to students and researchers working in related areas of mathematics and physics.’

Source: European Mathematical Society

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