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INTEGRATION FORMULAS INVOLVING FOURIER-FEYNMAN TRANSFORMS VIA A FUBINI THEOREM
Huffman, Timothy,Skoug, David,Storvick, David Korean Mathematical Society 2001 대한수학회지 Vol.38 No.2
In this paper we use a general Fubini theorem established in [13] to obtain several Feynman integration formulas involving analytic Fourier-Feynman transforms. Included in these formulas is a general Parseval's relation.
A FUBINI THEOREM FOR ANALYTIC FEYNMAN INTEGRALS WITH APPLICATIONS
Huffman, Timothy,Skoug, David,Storvick, David Korean Mathematical Society 2001 대한수학회지 Vol.38 No.2
In this paper we establish a Fubini theorem for various analytic Wiener and Feynman integrals. We then proceed to obtain several integration formulas as corollaries.
REFLECTION PRINCIPLES FOR GENERAL WIENER FUNCTION SPACES
Pierce, Ian,Skoug, David Korean Mathematical Society 2013 대한수학회지 Vol.50 No.3
It is well-known that the ordinary single-parameter Wiener space exhibits a reflection principle. In this paper we establish a reflection principle for a generalized one-parameter Wiener space and apply it to the integration of a class of functionals on this space. We also discuss several notions of a reflection principle for the two-parameter Wiener space, and explore whether these actually hold.
Further Results involving the Hilbert Space L2a,b[0, T]
최재길,David Skoug 한국수학교육학회 2020 純粹 및 應用數學 Vol.27 No.1
In this paper we determine conditions which a function a(t) must sat- isfy to insure that the function a′(t) is an element of the separable Hilbert space L2a,b[0, T]. We then proceed to illustrate our results with several pertinent examples and counter-examples.
Reflection principles for general Wiener function spaces
Ian Pierce,David Skoug 대한수학회 2013 대한수학회지 Vol.50 No.3
It is well-known that the ordinary single-parameter Wiener space exhibits a reflection principle. In this paper we establish a reflection principle for a generalized one-parameter Wiener space and apply it to the integration of a class of functionals on this space. We also discuss several notions of a reflection principle for the two-parameter Wiener space, and explore whether these actually hold.
ADMIXABLE OPERATORS AND A TRANSFORM SEMIGROUP ON ABSTRACT WIENER SPACE
장승준,최재길,David Skoug 대한수학회 2015 대한수학회지 Vol.52 No.1
The purpose of this paper is first of all to investigate the behavior of admixable operators on the product of abstract Wiener spaces and secondly to examine transform semigroups which consist of admix- Wiener transforms on abstract Wiener spaces.
The behavior of conditional Wiener integrals on product Wiener space
Choi, Jae Gil,Skouge, David,Chang, Seung Jun WILEY‐VCH Verlag 2013 Mathematische Nachrichten Vol.286 No.11
<P><B>Abstract</B></P><P>In this paper we first investigate the behavior of conditional Wiener integrals on product Wiener spaces and then proceed to establish a Fubini theorem for conditional Wiener integrals. We then define a very general multiple conditional analytic Fourier‐Feynman transform and a multiple conditional analytic convolution product for functionals on Wiener space and then establish a relationship between them. Next we obtain a basic formula for the conditional Wiener integral involving the first variation and the <I>n</I>‐dimensional Wiener directional derivative. Finally we establish several evaluation formulas for conditional Wiener and Feynman integrals involving the <I>n</I>‐dimensional Wiener directional derivative of functionals on Wiener space.</P>