Feynman's operational calculus for a sequential operator-valued function space integral (Q5948311)

The authors study Feynman's operational calculus and change of scale for the sequential operator-valued function space integral as a bounded linear operator from \(L_2(\mathbb R)\) into itself. They define operations \(*\) and \(\dotplus\) on functionals defined on \(S[0,t]\), the space of all piecewise continuous functions on \([0,t]\) and investigate the algebraic properties of these operations. They show that the sequential operator-valued function space integral of \(F * G\) is the product of the integrals of \(F\) and \(G\) and that the integral of the commutator of \(F\) and \(G\) is the commutator of the integrals of \(F\) and \(G\). Finally, they give a formula for change of scale for this integral.