In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. We first develop an operator version of the Henstock-Kurzweil integral, and a new Hilbert space that allows us to construct the elementary path integral in the manner originally envisioned by Feynman. After developing our time-ordered operator theory we extend a few of the important theorems of...

We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of δ-fine partitions by excluding small sets.