Contains both classical and modern methods in summability theory
Focuses on the basic developments concerning an idea in full details
Integrates theories as well as applications, wherever possible
This book discusses recent developments in and contemporary research on summability theory, including general summability methods, direct theorems on summability, absolute and strong summability, special methods of summability, functional analytic methods in summability, and related topics and applications. All contributing authors are eminent scientists, researchers and scholars in their respective fields, and hail from around the world.
Summability theory is generally used in analysis and applied mathematics. It plays an important part in the engineering sciences, and various aspects of the theory have long since been studied by researchers all over the world.
Audience
The book can be used as a textbook for graduate and senior undergraduate students, and as a valuable reference guide for researchers and practitioners in the fields of summability theory and functional analysis.
Topics
Sequences, Series, Summability
Functional Analysis
Approximations and Expansions
Author(s): Hemen Dutta, Billy E. Rhoades (eds.)
Edition: 1
Publisher: Springer
Year: 2016
Language: English
Pages: C, XII,431
Tags: Sequences, Series, Summability; Functional Analysis; Approximations and Expansions
Front Matter....Pages i-xiii
An Introduction to Summability Methods....Pages 1-27
Some Topics in Summability Theory....Pages 29-75
Summability and Convergence Using Ideals....Pages 77-140
Convergence Acceleration and Improvement by Regular Matrices....Pages 141-180
On Summability, Multipliability, and Integrability....Pages 181-239
Multi-dimensional Summability Theory and Continuous Wavelet Transform....Pages 241-311
Absolute Riesz and Related Summability Methods....Pages 313-355
Some Applications of Summability Theory....Pages 357-411
Degree of Approximation of Functions Through Summability Methods....Pages 413-431