tauberian theory a century of developments grundlehren der mathematischen wissenschaften

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Tauberian Theory

Author : Jacob Korevaar
ISBN : 9783662102251
Genre : Mathematics
File Size : 47. 73 MB
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Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book.

Introduction To Analytic And Probabilistic Number Theory

Author : Gérald Tenenbaum
ISBN : 9780821898543
Genre : Number theory
File Size : 49. 83 MB
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This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. --Mathematical Reviews

Function Spaces And Partial Differential Equations

Author : Ali Taheri
ISBN : 9780191047824
Genre : Mathematics
File Size : 54. 71 MB
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This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Mathematical Reviews

Author :
ISBN : UOM:39015067193329
Genre : Mathematics
File Size : 50. 43 MB
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Internationale Mathematische Nachrichten

Author :
ISBN : CORNELL:31924099691044
Genre : Mathematics
File Size : 90. 51 MB
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Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.

Newsletter

Author : New Zealand Mathematical Society
ISBN : UOM:39015060913897
Genre : Mathematics
File Size : 69. 83 MB
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Scientific And Technical Books In Print

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ISBN : UOM:39015035608390
Genre : Engineering
File Size : 72. 95 MB
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Evolution Equations

Author : David Ellwood
ISBN : 9780821868614
Genre : Mathematics
File Size : 60. 53 MB
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This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

The Lll Algorithm

Author : Phong Q. Nguyen
ISBN : 9783642022951
Genre : Computers
File Size : 58. 11 MB
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The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.

The Physics Of The Universe

Author : Sir James Hopwood Jeans
ISBN : UOM:39015077911116
Genre :
File Size : 87. 10 MB
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