Functional Inequalities Markov Semigroups and Spectral Theory
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.
The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle.
To get such a pragmatic mastery of inequalities, you surely need a comprehensive knowledge of basic inequalities at first. The goal of the first part of the book (chapters 1-8) is to lay down the foundations you will need in the second part (chapter g), here solving problems will give you some practice. It is important to try and solve the problems by yourself as hard as you can, since only practice will develop your understanding, especially the problems in the second part.
Explaining theory and research in an accessible but thorough manner, Gender and Social Psychology critically evaluates the contribution that psychology has made to the study of gender, examining key issues such as family roles and parenting, inequalities in education, jobs and pay, and the effects of media representation of the sexes.
