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Functional Analysis
Introduction to Further Topics in Analysis
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Format: Hardback
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See moreBeginning with the basic facts of functional analysis, this title looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. It uses the Baire category theorem to illustrate several points, including the existence of Besicovitch sets.
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Description
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, highlighting 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.
Functional Analysis offers a comprehensive and authoritative treatment of some of the main topics of modern analysis. It provides a look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables, discussing key results in each area in relation to other areas of mathematics and highlighting the organic unity of large areas of analysis traditionally split into subfields.
The book contains interesting exercises and problems that illustrate ideas, along with clear proofs to aid understanding.
Book Hero Magic summarised reviews for this book. While it's new and still learning, it may not be perfect - your feedback is welcome! HOW HAS THIS BEEN REVIEWED?
Functional Analysis by Rami Shakarchi and Elias M. Stein is praised for its fast-paced and comprehensive approach, making complex topics in functional analysis and related fields accessible to graduate students. It is commended for rewarding diligent readers with rich insights and applicable knowledge, touching on various branches like mathematical analysis and partial differential equations. The book is highly recommended for both students and educators as an invaluable resource for learning and teaching.
Book Details
INFORMATION
ISBN: 9780691113876
Publisher: Princeton University Press
Format: Hardback
Date Published: 11 September 2011
Country: United States
Imprint: Princeton University Press
Illustration: 27 line illus.
Audience: Tertiary education, Professional and scholarly
DIMENSIONS
Width: 152.0mm
Height: 235.0mm
Weight: 482g
Pages: 448
About the Author
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).
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Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here, the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series...Hardback$33300Unit price /UnavailableAvailableShips in 2-3 weeks -
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This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences—that an arbitrary function can be written as...HardbackSold Out -
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With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to...HardbackSold Out
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