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Hilbert space --- Selfadjoint operators --- Spectral theory (Mathematics) --- Functional analysis --- Measure theory --- Transformations (Mathematics) --- Operators, Selfadjoint --- Self-adjoint operators --- Linear operators --- Banach spaces --- Hyperspace --- Inner product spaces --- Hilbert space. --- Selfadjoint operators. --- Spectral theory (Mathematics).
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Nonselfadjoint operators --- Compact operators --- 517.983 --- Non-self-adjoint operators --- Operators, Non-self-adjoint --- Operators, Nonselfadjoint --- Linear operators --- Compact transformations --- Completely continuous operators --- Operators, Compact --- Operators, Completely continuous --- Transformations, Compact --- Linear operators. Linear operator equations --- Compact operators. --- Nonselfadjoint operators. --- 517.983 Linear operators. Linear operator equations --- Opérateurs linéaires. --- Linear operators. --- Fredholm, Opérateurs de --- Fredholm operators --- Opérateurs compacts --- Opérateurs linéaires. --- Fredholm, Opérateurs de --- Opérateurs compacts. --- Fredholm, Opérateurs de.
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The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Nonselfadjoint operators. --- Spectral theory (Mathematics) --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Non-self-adjoint operators --- Operators, Non-self-adjoint --- Operators, Nonselfadjoint --- Linear operators --- Functions of complex variables. --- Differential equations, partial. --- Differential Equations. --- Operator theory. --- Functions of a Complex Variable. --- Several Complex Variables and Analytic Spaces. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Operator Theory. --- 517.91 Differential equations --- Differential equations --- Partial differential equations --- Complex variables --- Elliptic functions --- Functions of real variables --- Differential equations. --- Partial differential equations.
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This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others. This interdisciplinary approach makes the book interesting to a large mathematical audience. Contributors: G. Baumslag A.V. Borovik T. Delzant W. Dicks E. Formanek R. Grigorchuk M. Gromov P. de la Harpe A. Lubotzky W. Lück A.G. Myasnikov C. Pache G. Pisier A. Shalev S. Sidki E. Zelmanov.
Infinite groups. --- Ergodic theory. --- Selfadjoint operators. --- Differential topology. --- Geometry, Differential --- Topology --- Operators, Selfadjoint --- Self-adjoint operators --- Linear operators --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Groups, Infinite --- Group theory --- Group theory. --- Topological Groups. --- Combinatorics. --- Operator theory. --- Global differential geometry. --- Algebraic topology. --- Group Theory and Generalizations. --- Topological Groups, Lie Groups. --- Operator Theory. --- Differential Geometry. --- Algebraic Topology. --- Functional analysis --- Combinatorics --- Algebra --- Mathematical analysis --- Groups, Topological --- Groups, Theory of --- Substitutions (Mathematics) --- Topological groups. --- Lie groups. --- Differential geometry. --- Differential geometry --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups
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The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem). Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises.
Selfadjoint operators. --- Hilbert space. --- Banach spaces --- Hyperspace --- Inner product spaces --- Operators, Selfadjoint --- Self-adjoint operators --- Linear operators --- Selfadjoint operators --- Hilbert space --- Operator theory --- Spectral theory (Mathematics) --- Opérateurs auto-adjoints --- Hilbert, Espaces de --- Opérateurs, Théorie des --- Théorie spectrale (mathématiques) --- Functional analysis. --- Mathematical physics. --- Operator theory. --- Functional Analysis. --- Mathematical Methods in Physics. --- Operator Theory. --- Mathematical Physics. --- Theoretical, Mathematical and Computational Physics. --- Functional analysis --- Physical mathematics --- Physics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Opérateurs auto-adjoints. --- Hilbert, Espaces de. --- Opérateurs, Théorie des. --- Mathematics. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Opérateurs auto-adjoints. --- Opérateurs, Théorie des. --- Théorie spectrale (mathématiques)
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Operator theory --- Differential operators --- Selfadjoint operators --- Spectral theory (Mathematics) --- 51 --- Boundary value problems --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Operators, Selfadjoint --- Self-adjoint operators --- Linear operators --- Operators, Differential --- Differential equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Mathematics --- 51 Mathematics --- Équations différentielles --- Théorie spectrale (mathématiques) --- Opérateurs linéaires --- Opérateurs auto-adjoints --- Differential equations. --- Linear operators. --- Selfadjoint operators. --- Équations différentielles. --- Opérateurs auto-adjoints --- Opérateurs linéaires --- Théorie spectrale (mathématiques) --- Problèmes aux limites --- Sturm liouville theory
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517.98 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Nonselfadjoint operators. --- Hilbert space --- Nonselfadjoint operators --- Non-self-adjoint operators --- Operators, Non-self-adjoint --- Operators, Nonselfadjoint --- Linear operators --- Banach spaces --- Hyperspace --- Inner product spaces --- Operator theory --- Hilbert space. --- Determinants. --- Déterminants (mathématiques) --- Opérateurs linéaires. --- Formes normales (mathématiques) --- Normal forms (Mathematics) --- Déterminants (mathématiques) --- Analyse fonctionnelle --- Functional analysis --- Opérateurs linéaires. --- Formes normales (mathématiques) --- Functional analysis. --- Opérateurs linéaires --- Linear operators. --- Operateurs lineaires hilbertiens --- Espaces d'operateurs lineaires continus --- Ideaux normes
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Mathematical physics --- Physique mathématique --- 517.98 --- Physical mathematics --- Physics --- Functional analysis and operator theory --- Mathematics --- Mathematical physics. --- 517.98 Functional analysis and operator theory --- Physique mathématique --- 517.983 --- 517.983 Linear operators. Linear operator equations --- Linear operators. Linear operator equations --- 517.44 --- #WWIS:ANAL --- 517.44 Integral transforms. Operational calculus. Laplace transforms. Fourier integral. Fourier transforms. Convolutions --- Integral transforms. Operational calculus. Laplace transforms. Fourier integral. Fourier transforms. Convolutions --- Operator theory --- Harmonic analysis. Fourier analysis --- Analyse fonctionnelle --- Functional analysis --- Fourier, Analyse de --- Functional analysis. --- Schroedinger operator --- Perturbation theory in quantum mechanics --- Operators(Non Self Adjoint-/Spectral Analysis) --- Spectral analysis of non self adjoint operators --- Operators(Self Adjoint-/Spectral Analysis) --- Spectral analysis of self adjoint operators --- Fourier transform --- Functional analysis in physics --- Operator extensions(Symmetric-) --- Semi groups of operators --- Operators(Self Adjoint-) --- Scattering in quantum field theory --- Scattering of non linear waves --- Scattering in quantum mechanics --- Light scattering --- Sound scattering --- Lax-Philips method in scattering theory --- Scattering theory --- Schroedinger operator in scattering theory --- Operateurs hilbertiens
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