Commun. Korean Math. Soc. 1997; 12(2): 293-303
Printed June 1, 1997
Copyright © The Korean Mathematical Society.
Bong Jin Kim, Kun Sik Ryu
Dae Jin University, Hannam University
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
2022; 37(3): 749-763
2000; 15(4): 715-721
2001; 16(4): 691-701
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd