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Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Advanced undergraduates and graduate students will find that this book presents a unique introduction to operators and Hilbert space.

Hilbert space. --- Banach spaces --- Hyperspace --- Inner product spaces --- Opérateurs compacts --- Compact operators --- Operateurs lineaires hilbertiens --- Theorie spectrale --- Espaces de hilbert

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Spectral theory (Mathematics) --- Spectre (Mathématiques) --- #KVIV:BB --- 517.984 --- 517.984 Spectral theory of linear operators --- Spectral theory of linear operators --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Spectral theory (Mathematics). --- Spectre (Mathématiques)

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Mathematical analysis --- Getaltheorie --- Mathematical sequences --- Nombres [Theorie des ] --- Number theory --- Numerical sequences --- Numerieke reeksen --- Reeksen (Wiskunde) --- Sequences (Mathematics) --- Spectra (Wiskunde) --- Spectral theory (Mathematics) --- Spectre (Mathematiques) --- Suites (Mathématiques) --- Suites numériques --- Wiskundige reeksen --- Number theory. --- 51 --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Algebra --- Mathematics --- Number study --- Numbers, Theory of --- 51 Mathematics

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This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, Lsup estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Harmonic analysis. Fourier analysis --- Harmonic analysis --- Analyse harmonique --- Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groupe de Heisenberg. --- Addition. --- Analytic function. --- Asymptote. --- Asymptotic analysis. --- Asymptotic expansion. --- Asymptotic formula. --- Automorphism. --- Axiom. --- Banach space. --- Bessel function. --- Big O notation. --- Bilinear form. --- Borel measure. --- Boundary value problem. --- Bounded function. --- Bounded mean oscillation. --- Bounded operator. --- Boundedness. --- Cancellation property. --- Cauchy's integral theorem. --- Cauchy–Riemann equations. --- Characteristic polynomial. --- Characterization (mathematics). --- Commutative property. --- Commutator. --- Complex analysis. --- Convolution. --- Differential equation. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Dirac delta function. --- Dirichlet problem. --- Elliptic operator. --- Existential quantification. --- Fatou's theorem. --- Fourier analysis. --- Fourier integral operator. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fubini's theorem. --- Function (mathematics). --- Fundamental solution. --- Gaussian curvature. --- Hardy space. --- Harmonic function. --- Heisenberg group. --- Hilbert space. --- Hilbert transform. --- Holomorphic function. --- Hölder's inequality. --- Infimum and supremum. --- Integral transform. --- Interpolation theorem. --- Lagrangian (field theory). --- Laplace's equation. --- Lebesgue measure. --- Lie algebra. --- Line segment. --- Linear map. --- Lipschitz continuity. --- Locally integrable function. --- Marcinkiewicz interpolation theorem. --- Martingale (probability theory). --- Mathematical induction. --- Maximal function. --- Meromorphic function. --- Multiplication operator. --- Nilpotent Lie algebra. --- Norm (mathematics). --- Number theory. --- Operator theory. --- Order of integration (calculus). --- Orthogonality. --- Oscillatory integral. --- Poisson summation formula. --- Projection (linear algebra). --- Pseudo-differential operator. --- Pseudoconvexity. --- Rectangle. --- Riesz transform. --- Several complex variables. --- Sign (mathematics). --- Singular integral. --- Sobolev space. --- Special case. --- Spectral theory. --- Square (algebra). --- Stochastic differential equation. --- Subharmonic function. --- Submanifold. --- Summation. --- Support (mathematics). --- Theorem. --- Translational symmetry. --- Uniqueness theorem. --- Variable (mathematics). --- Vector field. --- Fourier, Analyse de --- Fourier, Opérateurs intégraux de