Single and Multiple Number Series

Alberto Debernardi Pinos is Lecturer at the Universitat Autònoma 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 Matemàtica 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.

• 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.