Functional inequalities, Markov semigroups and spectral theory [E-Book].
Wang, Feng-Yu.
Beijing ; New York : Science Press, c2005
1 online resource.
Dang dai jie chu qing nian ke xue wen ku
Full Text
In this book, the functional inequalities are introduced to describe: (i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap; (ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density; (iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.