Leseprobe
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Functional Analysis
Elias M. Stein, Rami Shakarchi
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject.
- A comprehensive and authoritative text that treats some of the main topics of modern analysis
- A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables
- Key results in each area discussed in relation to other areas of mathematics
- Highlights the organic unity of large areas of analysis traditionally split into subfields
- Interesting exercises and problems illustrate ideas
- Clear proofs provided
Kundenbewertungen
Special case, Existential quantification, Integration by parts, Poisson kernel, Dual space, Subset, Addition, Holomorphic function, Metric space, Division by zero, Fourier transform, Banach space, Dimension, Function space, Complex number, Probability space, Hilbert transform, Interval (mathematics), Schwartz space, Quantity, Mathematics, Support (mathematics), Bessel function, Unit sphere, Bounded function, Corollary, Cauchy–Riemann equations, Lebesgue integration, Analytic continuation, Baire category theorem, Natural number, Smoothness, Scientific notation, Brownian motion, Continuous function, Derivative, Integer, Sign (mathematics), Summation, Probability theory, Change of variables, Theory, Estimation, Polynomial, Big O notation, Theorem, Compact space, Equation, Calculation, Hilbert space, Continuous function (set theory), Complex analysis, Convolution, Fubini's theorem, Maximal function, Bijection, Borel set, Measure (mathematics), Independence (probability theory), Fourier series, Characteristic function (probability theory), Differentiable function, Hardy space, Linear map, Fundamental solution, Lebesgue measure, Partial derivative, Partition of unity, Infimum and supremum, Dirac delta function