An Introductory Course in Summability Theory

Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book An Introductory Course in Summability Theory by Ants Aasma, Hemen Dutta, P. N. Natarajan, Wiley
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Ants Aasma, Hemen Dutta, P. N. Natarajan ISBN: 9781119397779
Publisher: Wiley Publication: April 5, 2017
Imprint: Wiley Language: English
Author: Ants Aasma, Hemen Dutta, P. N. Natarajan
ISBN: 9781119397779
Publisher: Wiley
Publication: April 5, 2017
Imprint: Wiley
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Wiley

Cover of the book High-Payoff Strategies by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book Management of Complex Cardiovascular Problems by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book Sex Cultures by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book Forward-Time Population Genetics Simulations by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book Aerosol Science by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book The Greening of Pharmaceutical Engineering, Theories and Solutions by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book First Aid For Pets For Dummies®, Portable Edition by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book The Business of Event Planning by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book Sustainable Manufacturing by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book Cyclopropanes in Organic Synthesis by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book The Marketing Century by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book Basic Option Volatility Strategies by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book Million-Dollar Hire by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book The Wiley-Blackwell Handbook of Disordered Gambling by Ants Aasma, Hemen Dutta, P. N. Natarajan
Cover of the book SharePoint 2016 For Dummies by Ants Aasma, Hemen Dutta, P. N. Natarajan
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy