Generalized multiresolution analyses (Q1790704)

This short monograph is based on the author's contributions to the area of (generalized) multiresolution analyses and is written in a lecture notes style. The book begins with the definition of generalized multiresolution analysis (GMRA) and a discussion of their properties. It proceeds by presenting more advanced topics such as the multiplicity and dimension functions of GMRAs, wavelets sets generated by dilation-translations pairs, generalized filters, fractal spaces, and abstract constructions of GMRAs beyond the \(L^2(\mathbb{R}^n)\)-setting. At the end of each lecture, references are given to the appropriate literature. This book provides the prospective reader with the tools and the framework to employ GMRAs and to possibly extend some results to more abstract settings. Readers should be familiar with a graduate level knowledge of real and functional analysis and some harmonic analysis. It is well-suited for graduate students who want to become familiar with this interesting topic and to researchers who would like to get a quick overview over the area.