Analysis and Geometry of Markov Diffusion Operators

“The book is friendly written and is of a rich content. With simple examples, main ideas of the study are clearly explained and naturally extended to a general framework, so that main progress in the field made for the past decades is presented in a smooth way. The monograph is undoubtedly a significant reference for further development of diffusion semigroups and related topics.” (Feng-Yu Wang, zbMATH 1376.60002, 2018)

“It is extremely rich. It is more original and inspirational than a treatise. One can use it and benefit from it in many ways: as a reference book, as an inspiration source, by focusing on a property or on an example. … From the beginning to the end, this book definitely has a strong personality and a characteristic taste. … anybody who wants to explore analytic, probabilistic or geometric properties of Markov semigroupsto have a look at it first.” (Thierry Coulhon, Jahresbericht der Deutschen Math-Vereinigung, Vol. 119, 2017)

“This impressive monograph is about an important and highly active area that straddles the fertile land occupied by both probability and analysis. … It is written with great clarity and style, and was clearly a labour of love for the authors. I am convinced that it will be a valuable resource for researchers in analysis and probability for many years to come.” (David Applebaum, The Mathematical Gazette, Vol. 100 (548), July, 2016)