• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.375-391
• /
• 1994

In 1968k Cameron and Storvick introduced the analytic and the sequential operator-valued function space integral [2]. Since then, the theo교 of the analytic operator-valued function space integral has been investigated by many mathematicians - Cameron, Storvick, Johnson, Skoug, Lapidus, Chang and author etc. But there are not that many papers related to the theory of the sequential operator-valued function space integral. In this paper, we establish the existence of the sequential operator-valued function space integral as an operator from $L_p$ to $L_p'(1 and investigated the integral equation related to this integral.

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.599-606
• /
• 1994

In [1], Cameron and Storvick introduced the analytic operator-valued function space integral. Johnson and Lapidus proved that this integral can be expressed in terms of an integral of operator-valued functions [6]. In this paper, we find some operator-valued Bochner integrable functions and prove that the analytic operator-valued function space integral of a certain function is represented as the Bochner integral of operator-valued functions on some conditions.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.791-802
• /
• 2000

In 1968, Cameron and Storvick introduce the definition and the theories of the operator-valued function space integral. Since then, the stability theorems of the integral was developed by Johnson, Skoug, Chang etc [1, 2, 4, 5]. Recently, the authors establish the existence theorem of the operator-valued function space [8]. In this paper, we will prove the stability theorems of the operator-valued function space integral over paths in abstract Wiener space $C_0(B)$.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.171-181
• /
• 1999

In this note, we will prove that the operator-valued function space integral as an operator from $L_p\;to\;L_{p'}$ (1

• Journal of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.73-86
• /
• 2003

In this paper, we define a generalized sequential operator-valued function space integral by using a generalized Wiener measure. It is an extention of the sequential operator-valued function space integral introduced by Cameron and Storvick. We prove the existence of this integral for functionals which involve some product Borel measures.

• Communications of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.293-303
• /
• 1997

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

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.465-475
• /
• 1996

Fix t > 0. Denote by $C^t$ the space of $R$-valued continuous functions x on [0,t]. Let $C_0^t$ be the Wiener space - $C_0^t = {x \in C^t : x(0) = 0}$ - equipped with Wiener measure m. Let F be a function from $C^t to C$.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.903-924
• /
• 2016

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.569-579
• /
• 1997

We investigate the existence of the operator-valued Feynman integral when a Wiener functional is given by a Fourier transform of complex Borel measure.

• Communications of the Korean Mathematical Society
• /
• v.17 no.1
• /
• pp.21-29
• /
• 2002

The existence of the operator-valued Feynman integral was established when a Wiener functional is given by a Fourier transform of complex Borel measures. In this paper, we investigate the stability of the Feynman integral with respect to the measures.