Operator theory and the Oka extension theorem

For δ an m-tuple of analytic functions, we define an algebra H_δ^∞_gen, contained in the bounded analytic functions on the analytic polyhedron (Formula Presented), and prove a representation formula for it. We give conditions whereby every function that is analytic on a neighborhood of (Formula Presented) is actually in H_δ^∞_gen. We use this to give a proof of the Oka extension theorem with bounds. We define an H_δ^∞_gen functional calculus for operators.