A01=Elias M. Stein
A01=Rami Shakarchi
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Author_Elias M. Stein
Author_Rami Shakarchi
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Baire category theorem
Banach space
Bessel function
Big O notation
Bijection
Borel set
Bounded function
Brownian motion
Calculation
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Cauchy-Riemann equations
Change of variables
Characteristic function (probability theory)
Compact space
Complex analysis
Complex number
Continuous function
Continuous function (set theory)
Convolution
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Derivative
Differentiable function
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Dirac delta function
Division by zero
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Existential quantification
Fourier series
Fourier transform
Fubini's theorem
Function space
Fundamental solution
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Hilbert space
Hilbert transform
Holomorphic function
Independence (probability theory)
Infimum and supremum
Integer
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Lebesgue integration
Lebesgue measure
Linear map
Mathematics
Maximal function
Measure (mathematics)
Metric space
Natural number
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Partition of unity
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Product details
- ISBN 9780691113876
- Weight: 748g
- Dimensions: 152 x 235mm
- Publication Date: 11 Sep 2011
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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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
Elias M. Stein is the Albert Baldwin Dod Professor of Mathematics at Princeton University. Rami Shakarchi received his PhD in mathematics from Princeton University. They are the coauthors of "Complex Analysis, Fourier Analysis", and "Real Analysis" (all Princeton).
