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Author: Jacob Korevaar
Publisher: Springer Science & Business Media
Published: 2004-05-26
Total Pages: 512
ISBN-13: 9783540210580
DOWNLOAD EBOOKThis book traces the development of Tauberian theory, evoking the excitement surrounding the early results. The author describes the fascination of the difficult Hardy-Littlewood theorems, and offers a new unified theory for Borel and "circle" methods.
Author: Alekseĭ Georgievich Postnikov
Publisher: American Mathematical Soc.
Published: 1980
Total Pages: 150
ISBN-13: 9780821830482
DOWNLOAD EBOOKAuthor: Jacob Korevaar
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 497
ISBN-13: 3662102250
DOWNLOAD EBOOKTauberian 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.
Author: J. van de Lune
Publisher:
Published: 1986
Total Pages: 120
ISBN-13:
DOWNLOAD EBOOKAuthor: V.S. Vladimirov
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 308
ISBN-13: 9400928319
DOWNLOAD EBOOKApproach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. The Scandal of Father G. K. Chesterton. 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: S. A. Mohiuddine
Publisher: Springer
Published: 2018-12-30
Total Pages: 248
ISBN-13: 9811330778
DOWNLOAD EBOOKThis book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. The theory of approximation deals with how functions can best be approximated with simpler functions. In the study of approximation of functions by linear positive operators, Bernstein polynomials play a highly significant role due to their simple and useful structure. And, during the last few decades, different types of research have been dedicated to improving the rate of convergence and decreasing the error of approximation.
Author: Hugh L. Montgomery
Publisher: Cambridge University Press
Published: 2007
Total Pages: 574
ISBN-13: 9780521849036
DOWNLOAD EBOOKA 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Author: Vasiliĭ Sergeevich Vladimirov
Publisher: American Mathematical Soc.
Published: 1988
Total Pages: 270
ISBN-13: 9780821831199
DOWNLOAD EBOOKAuthor: A. G. Postnikov
Publisher: American Mathematical Soc.
Published: 1988-12-31
Total Pages: 332
ISBN-13: 0821813498
DOWNLOAD EBOOKAimed at a level between textbooks and the latest research monographs, this book is directed at researchers, teachers, and graduate students interested in number theory and its connections with other branches of science. Choosing to emphasize topics not sufficiently covered in the literature, the author has attempted to give as broad a picture as possible of the problems of analytic number theory.
Author: Gérald Tenenbaum
Publisher: American Mathematical Soc.
Published: 2015-07-16
Total Pages: 656
ISBN-13: 082189854X
DOWNLOAD EBOOKThis 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
