Geodesic
Multiplicative Integration of Infinite Products
Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 692-698

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a complete normed abelian group with norm N 1. Let S be an interval (bounded or otherwise) of real numbers. We propose to study the Stieltjes integral equation where p is in G, a is in S, and each Fk is a function on S each value of which is a function from G to G. Our primary tools of investigation will be the works of J. S. MacNerney [6; 7] and their extensions by the author [4; 5]. Our main result, Theorem 4, will show that the equation above can be solved by a product integral of infinite products of solutions for the summands of the integrator. After obtaining our results, we shall specialize them to a linear situation and then show how this specialization allows us to obtain representations for analytic functions having only invertible values in a complex Banach algebra with identity. 
Lovelady, David Lowell. Multiplicative Integration of Infinite Products. Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 692-698. doi: 10.4153/CJM-1971-077-0
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