Single and Multiple Number Series (Encyclopedia of Mathematics and its Applications)

Debernardi Pinos, Alberto/ Liflyand, Elijah/ Tikhonov, Sergey

Cambridge University Press（2025/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 439 p.
• 言語 ENG
• 商品コード 9781009562997
• DDC分類 515.243

Full Description

Addressing a significant gap in the study of number series, this book presents an in-depth theory of multiple number series and an exhaustive examination of one-dimensional series. It incorporates overlooked yet essential results alongside recent research advancements. Much of the text is based on the authors' original contributions, particularly in the development of relaxed monotonicity concepts, which have become fundamental tools in Fourier and functional analysis. Each chapter concludes with historical context, aiding readers in understanding the theory's evolution. The book is aimed at a wide audience, ranging from undergraduate students to experts in the field. It offers a modern perspective on the theory, along with detailed introductory chapters that make complex concepts accessible for students. The audience will find the novel contributions enriching and inspiring.

Contents

Introduction; Part I. Single Series: 1. Generalized monotonicity; 2. Number series in dimension one; 3. Miscellaneous tests and results; Part II. Double Series: 4. Rudiments of double sequences and series; 5. Tests for convergence of double series; 6. Convergence tests involving generalizations of monotonicity; Part III. Multiple Series: 7. Rudiments of multiple sequences and series; 8. Tests for convergence of multiple series; 9. Multiple series with relaxed monotonicity; Table of correspondences; References - Monographs and Textbooks; References; Symbol index; Index.