Publisher: Cambridge University Press
Online publication date: April 2019
Print publication year: 2019
Online ISBN: 9781108654975
DOI: https://doi.org/10.1017/9781108654975
Subjects: Algebra, Fluid Dynamics and Solid Mechanics, Electronic,
Optoelectronic Devices, and Nanotechnology, Abstract Analysis, Mathematics
Series: Cambridge IISc Series
Publisher: Cambridge University Press
Online publication date: June 2019
Print publication year: 2019
Online ISBN: 9781108691550
DOI: https://doi.org/10.1017/9781108691550
Subjects: Particle Physics and Nuclear Physics, Physics And Astronomy,
Theoretical Physics and Mathematical Physics
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Publisher: Cambridge University Press
Online publication date: June 2016
Print publication year: 2016
Online ISBN: 9781107337145
DOI: https://doi.org/10.1017/CBO9781107337145
Series: Encyclopedia of Mathematics and its Applications (163)
Subjects: Logic, Categories and Sets, Recreational Mathematics,
Abstract Analysis, Mathematics
Publisher: Cambridge University Press
Expected online publication date: March 2020
Print publication year: 2020
Online ISBN: 9781139567718
Subjects: Recreational Mathematics, Geometry and Topology, Abstract Analysis, Mathematics
Series: New Mathematical Monographs (38)
This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further.
Publisher: Cambridge University Press
Expected online publication date: December 2019
Print publication year: 2019
Online ISBN: 9781139235723
Subjects: General Statistics and Probability, Physics And Astronomy, Statistics and Probability, Mathematical Methods, Statistics for Physical Sciences and Engineering
Series: Cambridge Series in Statistical and Probabilistic Mathematics (51)
Spectral analysis is widely used to interpret time series collected in diverse areas. This book covers the statistical theory behind spectral analysis and provides data analysts with the tools needed to transition theory into practice. Actual time series from oceanography, metrology, atmospheric science and other areas are used in running examples throughout, to allow clear comparison of how the various methods address questions of interest. All major nonparametric and parametric spectral analysis techniques are discussed, with emphasis on the multitaper method, both in its original formulation involving Slepian tapers and in a popular alternative using sinusoidal tapers. The authors take a unified approach to quantifying the bandwidth of nonparametric spectral estimate. An extensive set of exercises allows readers to test their understanding of theory and practical analysis. The time series used as examples and R language code for recreating the analyses of the series are available from the book's website.
Publisher: Cambridge University Press
Expected online publication date: January 2020
Print publication year: 2020
Online ISBN: 9781108584401
Subjects: Real and Complex Analysis, Recreational Mathematics, Abstract Analysis, Mathematics
Series: Cambridge Studies in Advanced Mathematics (184)
The last fifteen years have seen a flurry of exciting developments in Fourier restriction theory, leading to significant new applications in diverse fields. This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain?Guth induction on scales and the polynomial method. Also discussed in the second part are decoupling for curved manifolds and a wide variety of applications in geometric analysis, PDEs (Strichartz estimates on tori, local smoothing for the wave equation) and number theory (exponential sum estimates and the proof of the Main Conjecture for Vinogradov's Mean Value Theorem). More than 100 exercises in the text help reinforce these important but often difficult ideas, making it suitable for graduate students as well as specialists. Written by an author at the forefront of the modern theory, this book will be of interest to everybody working in harmonic analysis.
Publisher: Cambridge University Press
Expected online publication date: November 2019
Print publication year: 2019
Online ISBN: 9781108649711
Subjects: Number Theory, Recreational Mathematics, Mathematics
Series: London Mathematical Society Lecture Note Series (457)
This is the second volume of a series of mainly expository articles on the arithmetic theory of automorphic forms. It forms a sequel to On the Stabilization of the Trace Formula published by International Press in 2011. The books are intended primarily for two groups of readers: those interested in the structure of automorphic forms on reductive groups over number fields, and specifically in qualitative information on multiplicities of automorphic representations; and those interested in the classification of I-adic representations of Galois groups of number fields. Langlands' conjectures elaborate on the notion that these two problems overlap considerably. These volumes present convincing evidence supporting this, clearly and succinctly enough that readers can pass with minimal effort between the two points of view. Over a decade's worth of progress toward the stabilization of the Arthur-Selberg trace formula, culminating in Ngo Bau Chau's proof of the Fundamental Lemma, makes this series timely.
Publisher: Cambridge University Press
Expected online publication date: December 2019
Print publication year: 2019
Online ISBN: 9781108652865
Series: London Mathematical Society Student Texts (94)
Subjects: Discrete Mathematics Information Theory and Coding, Recreational Mathematics, Abstract Analysis, Mathematics
Approximate groups have shot to prominence in recent years, driven both by rapid progress in the field itself and by a varied and expanding range of applications. This text collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction. The author presents a number of recent developments in the field, including an exposition of his recent result classifying nilpotent approximate groups. The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples. It closes with a substantial chapter on applications, including an exposition of Breuillard, Green and Tao's celebrated approximate-group proof of Gromov's theorem on groups of polynomial growth. Written by an author who is at the forefront of both researching and teaching this topic, this text will be useful to advanced students and to researchers working in approximate groups and related areas.