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Classical and Modern Methods in Summability : Oxford Mathematical Monographs - Johann Boos

Classical and Modern Methods in Summability

Oxford Mathematical Monographs

Hardcover Published: 2nd November 2000
ISBN: 9780198501657
Number Of Pages: 600

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Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes of summability methods, Tauberian theorems, and applications of matrix methods. The proofs in Part I are exclusively done by applying classical analytical methods. Part II is concerned with modern functional analytical methods in summability, and contains the essential functional analytical basis required in later parts of the book, topologization of sequence spaces as K- and KF-spaces, domains of matrix methods as FK-spaces and their topological structure. In this part the proofs are of functional analytical nature only. Part III of the present book deals with topics in summability and topological sequence spaces which require the combination of classical and modern methods. It covers investigations of the constistency of matrix methods and of the bounded domain of matrix methods via Saks space theory, and the presentation of some aspects in topological sequence spaces. Lecturers, graduate students, and researchers working in summability and related topics will find this book a useful introduction and reference work.

Industry Reviews

" This book will serve as a strong stimulus to interest new researchers in summability" Zentralblatt Mathematik

Preface Part I: Classical methods in summability and applications 1: Convergence and divergence 2: Matrix methods: Basic classical theory 3: Special summability methods 4: Tauberian Theorems 5: Application of matrix methods Part II: Functional analytic methods in summability 6: Functional analytic basis 7: Topological sequence spaces: K- and FK-spaces 8: Matrix methods: Structure of the domains Part III: Combining classical and functional analytic methods 9: Consistency of matrix methods 10: Saks spaces and bounded domains 11: Some aspects of Topological Sequence Spaces Bibliography Index

ISBN: 9780198501657
ISBN-10: 019850165X
Series: Oxford Mathematical Monographs
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 600
Published: 2nd November 2000
Country of Publication: GB
Dimensions (cm): 23.39 x 15.6  x 3.33
Weight (kg): 1.02

Earn 601 Qantas Points
on this Book