Heat Kernels for Elliptic and Sub-elliptic Operators Methods and Techniques

From the reviews:

“The present book provides a comprehensive presentation of several theories for finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. One of the nice features of the book is the diversity of methods used, coming from the theory of stochastic processes, differential geometry, special functions, quantum mechanics and PDEs. … the book is very well organized and essentially self-contained. Hence, it is perfect reference material for graduate students and researchers in harmonic analysis and sub-Riemannian geometry, as well as theoretical physicists.” (Fabio Nicola, Mathematical Reviews, Issue 2011 i)

“Authors of the present monograph devote themselves to finding the explicit formulas of heat kernels for elliptic and sub-elliptic operators. … there are plenty of exact formulas of the heat kernels for elliptic and sub-elliptic operators in this work. Most of them are represented by means of elementary functions. … Those results in this book are important to the experts for further studying the diffusion phenomena or the properties of solutions of parabolic equations with initial data. … this is also a good reference book.” (Jun-Qi Hu, Zentralblatt MATH, Vol. 1207, 2011)