## Functional Analysis: |

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, - 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
" "Characteristically, Stein and Shakarchi reward readers for hard work by making the material pay off." "This excellent book ends with a proof of the continuity of the averaging operator and applications to the determination of remainder terms in asymptotic formulas for the counting function of lattice points. Reading this book is an enjoyable experience. The reviewer highly recommends it for students and professors interested in a clear exposition of these topics." "This book is accessible for graduate students. Moreover, it plays the role of an instructional book in various branches of mathematical analysis, geometry, probability, and partial differential equations. In most mathematical centers one cannot expect that such lectures will be offered as a semester-long course to students, but both students and teachers have here an excellent guide for learning and teaching the topics presented in this volume. . . . Reading this book is an enjoyable experience. The reviewer highly recommends it for students and professors interested in a clear exposition of these topics."
"This book introduces basic functional analysis, probability theory, and most importantly, aspects of modern analysis that have developed over the last half century. It is the first student-oriented textbook where all of these topics are brought together with lots of interesting exercises and problems. This is a valuable addition to the literature."
- Beijing Lectures in Harmonic Analysis. (AM-112). [Paperback]
- Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11). [Paperback]
- Complex Analysis. [Hardcover]
- Fourier Analysis: An Introduction. [Hardcover]
- Hardy Spaces on Homogeneous Groups. (MN-28). [Paperback]
- Harmonic Analysis (PMS-43): Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43). [Hardcover]
- Introduction to Fourier Analysis on Euclidean Spaces (PMS-32). [Hardcover]
- Lectures on Pseudo-Differential Operators: Regularity Theorems and Applications to Non-Elliptic Problems. (MN-24). [Paperback]
- Real Analysis: Measure Theory, Integration, and Hilbert Spaces. [Hardcover]
- Singular Integrals and Differentiability Properties of Functions (PMS-30). [Hardcover]
- Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63). [Paperback]
- Complex Analysis. [Hardcover]
- Fourier Analysis: An Introduction. [Hardcover]
- Real Analysis: Measure Theory, Integration, and Hilbert Spaces. [Hardcover]
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