An Introduction to Tauberian Theory
Author | : J. van de Lune |
Publisher | : |
Total Pages | : 120 |
Release | : 1986 |
Genre | : Fourier transformations |
ISBN | : |
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Author | : J. van de Lune |
Publisher | : |
Total Pages | : 120 |
Release | : 1986 |
Genre | : Fourier transformations |
ISBN | : |
Author | : Jacob Korevaar |
Publisher | : Springer Science & Business Media |
Total Pages | : 497 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662102250 |
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.
Author | : Alekseĭ Georgievich Postnikov |
Publisher | : American Mathematical Soc. |
Total Pages | : 150 |
Release | : 1980 |
Genre | : Mathematics |
ISBN | : 9780821830482 |
Author | : |
Publisher | : Academic Press |
Total Pages | : 272 |
Release | : 1971-09-30 |
Genre | : Mathematics |
ISBN | : 0080873553 |
An introduction to transform theory
Author | : Jacob Korevaar |
Publisher | : Springer Science & Business Media |
Total Pages | : 512 |
Release | : 2004-05-26 |
Genre | : Mathematics |
ISBN | : 9783540210580 |
This 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 | : Ants Aasma |
Publisher | : John Wiley & Sons |
Total Pages | : 220 |
Release | : 2017-04-03 |
Genre | : Mathematics |
ISBN | : 1119397731 |
An introductory course in summability theory for students, researchers, physicists, and engineers In creating this book, the authors’ intent was to provide graduate students, researchers, physicists, and engineers with a reasonable introduction to summability theory. Over the course of nine chapters, the authors cover all of the fundamental concepts and equations informing summability theory and its applications, as well as some of its lesser known aspects. Following a brief introduction to the history of summability theory, general matrix methods are introduced, and the Silverman-Toeplitz theorem on regular matrices is discussed. A variety of special summability methods, including the Nörlund method, the Weighted Mean method, the Abel method, and the (C, 1) - method are next examined. An entire chapter is devoted to a discussion of some elementary Tauberian theorems involving certain summability methods. Following this are chapters devoted to matrix transforms of summability and absolute summability domains of reversible and normal methods; the notion of a perfect matrix method; matrix transforms of summability and absolute summability domains of the Cesàro and Riesz methods; convergence and the boundedness of sequences with speed; and convergence, boundedness, and summability with speed. • Discusses results on matrix transforms of several matrix methods • The only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory • Compares the approximation orders of Fourier expansions in Banach spaces by different matrix methods • Matrix transforms of summability domains of regular perfect matrix methods are examined • Each chapter contains several solved examples and end-of-chapter exercises, including hints for solutions An Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation. ANTS AASMA, PhD, is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia. HEMEN DUTTA, PhD, is Senior Assistant Professor of Mathematics at Gauhati University, India. P.N. NATARAJAN, PhD, is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.
Author | : V.S. Vladimirov |
Publisher | : Springer Science & Business Media |
Total Pages | : 308 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400928319 |
Approach 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 | : Tord H. Ganelius |
Publisher | : Springer |
Total Pages | : 81 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540369791 |
Author | : |
Publisher | : |
Total Pages | : 134 |
Release | : 1960 |
Genre | : |
ISBN | : |
Author | : Manuel González |
Publisher | : Springer Science & Business Media |
Total Pages | : 253 |
Release | : 2010-01-09 |
Genre | : Mathematics |
ISBN | : 3764389982 |
This text offers a complete exposition of the theory of tauberian operators. It describes the origins of the subject in the study of summability of series, and it covers the most recent advances, emphasizing its applications to Banach space theory.