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 semigroups to 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)