Linear operators and their spectra / E. Brian Davies.

Author/creator Davies, E. B.
Format Book
Publication InfoCambridge : Cambridge University Press, 2007.
Descriptionxii, 451 pages ; 24 cm.
Subjects
Linear operators.
Spectral theory (Mathematics)

SeriesCambridge studies in advanced mathematics ; 106
Cambridge studies in advanced mathematics ; 106. ^A664587
Contents Cover -- Contents -- Preface -- 1 Elementary operator theory -- 1.1 Banach spaces -- 1.2 Bounded linear operators -- 1.3 Topologies on vector spaces -- 1.4 Differentiation of vector-valued functions -- 1.5 The holomorphic functional calculus -- 2 Function spaces -- 2.1 Lp spaces -- 2.2 Operators acting on Lp spaces -- 2.3 Approximation and regularization -- 2.4 Absolutely convergent Fourier series -- 3 Fourier transforms and bases -- 3.1 The Fourier transform -- 3.2 Sobolev spaces -- 3.3 Bases of Banach spaces -- 3.4 Unconditional bases -- 4 Intermediate operator theory -- 4.1 The spectral radius -- 4.2 Compact linear operators -- 4.3 Fredholm operators -- 4.4 Finding the essential spectrum -- 5 Operators on Hilbert space -- 5.1 Bounded operators -- 5.2 Polar decompositions -- 5.3 Orthogonal projections -- 5.4 The spectral theorem -- 5.5 Hilbert-Schmidt operators -- 5.6 Trace class operators -- 5.7 The compactness of f(Q)g(P) -- 6 One-parameter semigroups -- 6.1 Basic properties of semigroups -- 6.2 Other continuity conditions -- 6.3 Some standard examples -- 7 Special classes of semigroup -- 7.1 Norm continuity -- 7.2 Trace class semigroups -- 7.3 Semigroups on dual spaces -- 7.4 Differentiable and analytic vectors -- 7.5 Subordinated semigroups -- 8 Resolvents and generators -- 8.1 Elementary properties of resolvents -- 8.2 Resolvents and semigroups -- 8.3 Classification of generators -- 8.4 Bounded holomorphic semigroups -- 9 Quantitative bounds on operators -- 9.1 Pseudospectra -- 9.2 Generalized spectra and pseudospectra -- 9.3 The numerical range -- 9.4 Higher order hulls and ranges -- 9.5 Von Neumann's theorem -- 9.6 Peripheral point spectrum -- 10 Quantitative bounds on semigroups -- 10.1 Long time growth bounds -- 10.2 Short time growth bounds -- 10.3 Contractions and dilations -- 10.4 The Cayley transform -- 10.5 One-parameter groups -- 10.6 Resolvent bounds in Hilbert space -- 11 Perturbation theory -- 11.1 Perturbations of unbounded operators -- 11.2 Relatively compact perturbations -- 11.3 Constant coefficient differential operators on the half-line -- 11.4 Perturbations: semigroup based methods -- 11.5 Perturbations: resolvent based methods -- 12 Markov chains and graphs -- 12.1 Definition of Markov operators -- 12.2 Irreducibility and spectrum -- 12.3 Continuous time Markov chains -- 12.4 Reversible Markov semigroups -- 12.5 Recurrence and transience -- 12.6 Spectral theory of graphs -- 13 Positive semigroups -- 13.1 Aspects of positivity -- 13.2 Invariant subsets -- 13.3 Irreducibility -- 13.4 Renormalization -- 13.5 Ergodic theory -- 13.6 Positive semigroups on C(X) -- 14 NSA Schrödinger operators -- 14.1 Introduction -- 14.2 Bounds on the numerical range -- 14.3 Bounds in one space dimension -- 14.4 The essential spectrum of Schrödinger operators -- 14.5 The NSA harmonic oscillator -- 14.6 Semi-classical analysis -- References -- Index -- Last Page.
Review "This wide-ranging and self-contained account of this spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises."--Jacket.
Bibliography noteIncludes bibliographical references and index.
LCCN 2007279864
ISBN9780521866293
ISBN0521866294

Availability

Library Location Call Number Status Item Actions
Joyner General Stacks QA329.2 .D385 2007 ✔ Available Place Hold