Product integrals II: Contour integrals

AbstractThis paper continues the joint work of the authors begun in the article “On Strong Product Integration” [J. Functional Analysis, submitted]. We consider product integrals along contours; the point of view and development is analogous to the usual complex variable theory of ordinary contour integrals. Our main results are Theorem 2.3 (homotopy invariance of product integrals, an analog of Cauchy's integral theorem) and Theorem 3.4 (an analog of Cauchy's integral formula or the residue theorem)