# RELATIONSHIPS BETWEEN INTEGRAL TRANSFORMS AND CONVOLUTIONS ON AN ANALOGUE OF WIENER SPACE

Cho, Dong Hyun

• Received : 2013.01.13
• Accepted : 2013.01.28
• Published : 2013.03.25
• 27 4

#### Abstract

In the present paper, we evaluate the analytic conditional Fourier-Feynman transforms and convolution products of unbounded function which is the product of the cylinder function and the function in a Banach algebra which is defined on an analogue o Wiener space and useful in the Feynman integration theories and quantum mechanics. We then investigate the inverse transforms of the function with their relationships and finally prove that th analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function.

#### Keywords

analogue of Wiener space;analytic conditional Feynman integral;analytic conditional Fourier-Feynman transform;conditional convolution product;conditional Wiener integral;Wiener space

#### References

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#### Acknowledgement

Supported by : National Research Foundation(NRF)