Harmonic Analysis And Fractal Analysis Over Local Fields And Applications

This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975, regarded as the first monograph in this research field. The book is self-contained, with wide scope and deep knowledge, taking modern mathematics such as modern algebra, point set topology, functional analysis, distribution theory, and so on as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. The author aims to make those difficult concepts accessible to readers, illustrating clear comparisons between harmonic analysis on Euclidean spaces and that on local fields, and providing motivations underlying the new concepts and techniques. Overall, it is a high-quality, up-to-date, and valuable book for interested readers, including undergraduate students, graduate students, and researchers.