Communications of the
Korean Mathematical Society CKMS

The existence theorem for the operator valued function space integral has been studied, when the wave function was in $ L_1(\Bbb R) $ class and the potential energy function was represented as a double integral [4]. Johnson and Lapidus established the existence theorem for the operator valued function space integral, when the wave function was in $ L_2 (\Bbb R) $ class and the potential energy function was represented as an integral involving a Borel measure [9]. In this paper, we establish the existence theorem for the operator valued function space integral as an operator from $L_1(\Bbb R)$ to $L_\infty (\Bbb R)$ for certain potential energy functions which involve double integrals with some Borel measures.

Keywords: Wiener measure, function space integral

MSC numbers: 28C20