A MULTIPLE GENERALIZED FOURIER-FEYNMAN TRANSFORM VIA A ROTATION ON WIENER SPACE

被引：19

作者：

Choi, Jae Gil ^{[1
]}

Skoug, David ^{[2
]}

Chang, Seung Jun ^{[1
]}

机构：

[1] Dankook Univ, Dept Math, Cheonan 330714, South Korea

[2] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2012年 / 23卷 / 07期

基金：

新加坡国家研究基金会;

关键词：

Paley-Wiener-Zygmund stochastic integral; Gaussian process; generalized Fourier-Feynman transform; multiple generalized Fourier-Feynman transform; generalized convolution product; CONVOLUTION;

D O I：

10.1142/S0129167X12500681

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we use a rotation property of Wiener measure to define a very general multiple Fourier-Feynman transform on Wiener space. We then proceed to establish its many algebraic properties as well as to establish several relationships between this generalized multiple transform and the corresponding generalized convolution product.

引用

页数：20

共 43 条

[31] Sequential Fourier-Feynman transform, convolution and first variation
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Cho, D. H.
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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (04) : 1819 - 1838
[32] FOURIER-FEYNMAN TRANSFORMS FOR FUNCTIONALS IN A GENERALIZED FRESNEL CLASS
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[33] Parts formulas involving the Fourier–Feynman transform associated with Gaussian paths on Wiener space
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[34] Analytic Fourier-Feynman transforms associated with bounded linear operators on abstract Wiener spaces
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[35] Relationship Between the Analytic Generalized Fourier–Feynman Transform and the Function Space Integral
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Results in Mathematics, 2021, 76
[36] GENERALIZED FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS FOR EXPONENTIAL TYPE FUNCTIONS OF GENERALIZED BROWNIAN MOTION PATHS
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[37] CHANGE OF SCALE FORMULAS FOR FUNCTION SPACE INTEGRALS RELATED WITH FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION ON C-a,C- (b)[0, T]
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KOREAN JOURNAL OF MATHEMATICS, 2015, 23 (01): : 47 - 64
[38] Convolution and the Fourier-Wiener transform on abstract Wiener space
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[39] CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH INFINITE DIMENSIONAL CONDITIONING FUNCTION
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BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2023, 60 (05) : 1221 - 1235
[40] CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH VECTOR-VALUED CONDITIONING FUNCTION
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JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2023, 30 (02): : 155 - 167

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