Publisher's Synopsis
Positive definite functions and their generalizations have arisen in diverse parts of mathematics since the beginning of this century. They occur naturally in harmonic analysis, moment problems, operator theory, probability theory, and other areas. A considerable portion of our function-theoretical knowledge of locally compact groups rests upon a study of positive definite functions. The present book provides an introduction to the theory of these functions from the point of view of harmonic analysis on amps.;The first chapter deals with basic results on positive definite functions, the second one contains some applications. The third and fourth chapters are devoted to special questions: decomposition and extension of positive definite functions. The second part of the book (chapters 5 and 6) deals with functions having a finite number of negative squares and with definitizable functions. The appendix is a self-contained introduction to basic facts from the theory of Pontryagin spaces.
