Vector-valued positive definite functions, the Berg-Maserick theorem, and application

摘要

The theory of positive definite functions is an important and extensive area of modern mathematics, having many and varied applications. One of the fudamental results is the integral representation theorem for exponentially bounded, positive definite functions due to C. Berg and P. H. Maserick; see (4, Ch. 4 Section 2] and [5]. In order to formulate this result we require some terminology.