The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under v…
This is the second, completely revised and expanded edition of the author's first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book prese…
This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic…
This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a ne…
This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the stu…
This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Withi…
The textbook provides both profound technological knowledge and a comprehensive treatment of essential topics in music processing and music information retrieval (MIR). Including numerous examples, figures, and exercises, this book is suited for students, lecturers, and research…
Reflects the developments in the area of wavelet analysis and its applications. This work includes topics such as: Approximation and Fourier Analysis; Construction of Wavelets and Frame Theory; Fractal and Multifractal Theory; Wavelets in Numerical Analysis; Time-Frequency Analy…
