Vol. 34, No. 2, 1970

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Operator-valued Feynman integrals of finite-dimensional functionals

Gerald William Johnson and David Lee Skoug

Vol. 34 (1970), No. 2, 415–425

Let C[a,b] denote the space of continuous functions x on [a,b]. Let {α1,n} be an orthonormal set of functions of bounded variation on [a,b]. Let

        ∫ b             ∫ b
F(x) = f(a α1(t)dx(t),⋅⋅⋅ ,a αn (t)dx(t)).

Recently, Cameron and Storvick defined certain operator-valued function space integrals, and, in particular, an operator-valued Feynman integral. In their setting, we give existence theorems as well as explicit formulas for the function space integrals of functionals F as above. We also study the properties of the operators which arise by “integrating” this type of functional.

Mathematical Subject Classification
Primary: 47.70
Secondary: 28.00
Received: 22 August 1969
Published: 1 August 1970
Gerald William Johnson
David Lee Skoug