A moment problem for pseudo-positive definite functionals
This provides a theoretical extension of classical moment theory to signed measures, which is incremental for specialists in functional analysis and moment problems.
The paper solves a moment problem for pseudo-positive definite functionals by proving the existence of a representing pseudo-positive measure under reasonable restrictions, and characterizes determinacy in the class of equivalent representations.
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing pseudo-positive measure. The second main result is a characterization of determinacy in the class of equivalent pseudo-positive representation measures. Finally the corresponding truncated moment problem is discussed.