scholarly journals SOME RELATIONSHIPS BETWEEN THE INTEGRAL TRANSFORM AND THE CONVOLUTION PRODUCT ON ABSTRACT WIENER SPACE

2015 ◽  
Vol 31 (1) ◽  
pp. 135-144
Author(s):  
Jeong Eun Lee ◽  
Seung Jun Chang
Keyword(s):  
Integral Transform ◽  
Wiener Space ◽  
Convolution Product ◽  
Abstract Wiener Space

scholarly journals Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and Convolution

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Bong Jin Kim ◽  
Byoung Soo Kim ◽  
Il Yoo
Keyword(s):  
Banach Algebra ◽  
Wiener Space ◽  
Convolution Product ◽  
Abstract Wiener Space ◽  
Change Of Scale ◽  
Generalized Fresnel Class

Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in Banach algebraSon classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel classF(B)and in a generalized Fresnel classFA1,A2on abstract Wiener space. We express Fourier-Feynman transform and convolution product of functionals inSas limits of Wiener integrals. Moreover we obtain change of scale formulas for Wiener integrals related to Fourier-Feynman transform and convolution product of these functionals.

Conditional Fourier-Feynman Transform and Convolution Product Over Wiener Paths In Abstract Wiener Space

2003 ◽  
Vol 14 (3) ◽  
pp. 217-235 ◽  
Author(s):  
K. S. Chang ◽  
D. H. Cho ◽  
B. S. Kim ◽  
T. S. Song ◽  
I. Yoo
Keyword(s):  
Wiener Space ◽  
Convolution Product ◽  
Abstract Wiener Space

scholarly journals A Rotation of Admixable Operators on Abstract Wiener Space with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Jae Gil Choi ◽  
Seung Jun Chang
Keyword(s):  
Algebraic Structure ◽  
Wiener Measure ◽  
Wiener Space ◽  
Convolution Product ◽  
Abstract Wiener Space

We investigate certain rotation properties of the abstract Wiener measure. To determine our rotation property for the Wiener measure, we introduce the concept of an admixable operator via an algebraic structure on abstract Wiener space. As for applications, we define the analytic Fourier-Feynman transform and the convolution product associated with the admixable operators and proceed to establish the relationships between this transform and the corresponding convolution product.

scholarly journals The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 389
Author(s):  
Jeong-Gyoo Kim
Keyword(s):  
Hilbert Space ◽  
Fourier Series ◽  
Fourier Coefficients ◽  
Double Sequence ◽  
Intermediate Stage ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Abstract Space ◽  
Double Sequences ◽  
Two Parameter

Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences. We understand the space of double Fourier coefficients as an abstract space of sequences and examine relationships to spaces of general double sequences: p-power summable sequences for p = 1, 2, and the Hilbert space of double sequences. Using uniform convergence in the sense of a Cesàro mean, we verify the inclusion relationships between the four spaces of double sequences; they are nested as proper subsets. The completions of two spaces of them are found to be identical and equal to the largest one. We prove that the two-parameter Wiener space is isomorphic to the space of Cesàro means associated with double Fourier coefficients. Furthermore, we establish that the Hilbert space of double sequence is an abstract Wiener space. We think that the relationships of sequence spaces verified at an intermediate stage in this paper will provide a basis for the structures of those spaces and expect to be developed further as in the spaces of single-indexed sequences.

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