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.
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978-1-009-56299-7 (9781009562997)
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Schweitzer Klassifikation
Alberto Debernardi Pinos is Lecturer at the Universitat Autonoma de Barcelona. He has built a strong junior research career, gaining international experience through post-doctoral positions in Israel and Portugal. His research covers various fields, including Fourier analysis, sampling theory, approximation theory, and noncommutative analysis. Elijah Liflyand held various positions in the Department of Mathematics at Bar-Ilan University, Israel until his retirement in 2020. He has authored three books, including 'Harmonic Analysis on the Real Line' (2021), and edited three further volumes. His research interests include Fourier analysis, approximation, and several complex variables. Sergey Tikhonov is ICREA Research Professor at the Centre de Recerca Matematica in Barcelona. His main areas of interest include Fourier analysis and approximation theory. Maria Zeltser is Associate Professor at Tallinn University. She has made valuable contributions to the fields of sequence and double sequence spaces, as well as summability theory. She co-authored a widely used book on financial mathematics in 2020 and has practical experience as a data specialist and analyst.
Autor*in
Universitat Autonoma de Barcelona
Bar-Ilan University, Israel
Centre de Recerca Matematica, Barcelona
Tallinn University
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.
