Study at TCU


Name FURUTA Koji
Official Title Associate Professor
Affiliation Liberal Arts and Sciences
Profile My research is mainly concerned with integral representations of positive definite functions on commutative semigroups. It is well-known that a continuous positive definite function on a locally compact commutative group has a unique integral representation on its dual commutative group. In the contrary, a positive definite function on a commutative semigroup does not always have an integral representation, and even when the function has an integral representation, there is not always just one representing measure. The goal of my research is to elucidate the properties of semigroups in terms of the possibility of integral representations of positive definite functions.
Research Field(Keyword & Summary)
  1. positive definite functions on semigroups

    Positive definite functions on commutative semigroups are a common generalization of Laplace and Fourier transforms, moment sequences and related concepts. Its theory has many applications in various fields of mathematics, particularly in probability theory and statistics.

Representative Papers
  1. Integral representations of positive definite functions on convex sets of certain semigroups of rational numbers. Nihonkai Math. J. 28 (2017), no. 2
  2. A moment problem on rational numbers. Hokkaido Math. J. 46 (2017), no. 2
Grant-in-Aid for Scientific Research Support: Japan Society for Promotion of Science (JSPS)
Recruitment of research assistant(s) No
Affiliated academic society (Membership type) The Mathematical Society of Japan (Fellow)
Education Field (Undergraduate level) Mathematics
Education Field (Graduate level) Mathematics