The second volume delves into the fascinating realm of complex analysis, showcasing the elegance of holomorphic functions through foundational theorems like the Cauchy theorems and residues. It explores analytic continuation and the argument principle, while also bridging connections to other mathematical fields. Topics include the Fourier transform via contour integration, the zeta function in relation to the prime number theorem, and an introduction to elliptic functions, highlighting their applications in combinatorics and number theory.
"This book covers such topics as Lp spaces, distributions, Baire category, probability theory and Brownian motion, several complex variables and oscillatory integrals in Fourier analysis. The authors focus on key results in each area, highlighting their importance and the organic unity of the subject"--Provided by publisher.
Measure Theory, Integration, and Hilbert Spaces - Reprint Edition
402 stránek
15 hodin čtení
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 to make plain the organic unity that exists between the various parts of the subject and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidean spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.
. Publishing Pub Date :2012-12-01 311 The World Publishing Company Fourier Analysis Introduction - version of the original 59 yuan (U.S.) Stein book World Book Publishing Company published Date :2012-12-1
