Publisher's Synopsis
The central theme of this text is Khinchin-type representation theorems. An abstract framework for unimodality, an example of applied functional analysis, is developed for the introduction of different types of unimodality and the study of their behaviour. Also, several useful consequences or ramifications tied to these notions are provided.;This text aims to serve as an understanding of the basic features of unimodality. Chapter 1 lays a foundation for the mathematical reasoning in the chapters following. Chapter 2 deals with the concept of Khinchin space, which leads to the introduction of beta-unimodality in Chapter 3. A discussion on several existing multivariate notions of unimodality concludes this chapter. Chapter 4 concerns Khinchin's classical unimodality, and Chapter 5 is devoted to discrete unimodality. Chapters 6 and 7 treat the concept of strong unimodality on and to Ibragimov-type results characterizing the probability measures which preserve unimodality by convolution, and the concept of slantedness, respectively. Most chapters end with comments, referring to historical aspects or supplying complementary information and open questions. A practical bibliography, as well as symbol, name and subject indices ensure efficient use of this volume.
