Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series

This book discusses the theory of Vilenkin-Fourier series, which are rectangular waves used in signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing, and pattern recognition. It is influenced by the classical theory of trigonometric series and is related to modern abstract harmonic analysis. The first part of the book can be used as an introduction, and the following chapters summarize recent research. The book is intended for researchers working in Fourier and harmonic analysis and applied fields.

Format: Hardback
Length: 626 pages
Publication date: 23 November 2022
Publisher: Birkhauser Verlag AG

This comprehensive book delves into the theory of Vilenkin-Fourier series, a branch of modern harmonic analysis. It explores the decomposition of functions into sinusoidal waves, contrasting them with rectangular waves known as Vilenkin (Walsh) functions. These functions have found widespread applications in signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing, and pattern recognition. The development of the Vilenkin-Fourier series has been significantly influenced by the classical theory of trigonometric series, leading to inevitable comparisons between the two. While there are similarities between these theories, there are also notable differences, which can be explained through modern abstract harmonic analysis.

The first part of the book serves as an introduction to the subject, providing a solid foundation for further exploration. The subsequent chapters summarize the latest research in this captivating field, making them accessible to independent readers. Each chapter concludes with historical remarks and open questions, encouraging further discussion and research. This book appeals to researchers and scholars engaged in Fourier and broader harmonic analysis, as well as those working in applied fields. Its comprehensive nature and wealth of information make it a valuable resource for both novice and experienced researchers, inspiring them to pursue their own studies and contribute to the field.

Weight: 1124g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031144585
Edition number: 1st ed. 2022