A new aspect of the analytic Fourier-Feynman transform and its applications

Abstract

In this paper we define a modified analytic function space Fourier-Feynman transform to explain some physical phenomenon. We then establish various relationships involving the modified analytic function space Fourier-Feynman transform with related topics. Finally, we apply the translation theorem to obtain various relationships involving the modified analytic function space Fourier-Feynman transform. Our approach is a new and interesting method to explain some physical phenomenon.

Keywords:

• generalized Brownian motion process
• modified analytic function space Fourier-Feynman transform
• translation theorem
• diffusion equation
• Feynman–Kac formula
• Schrödinger equation

Mathematics Subject Classification:

• 28C20
• 60J65
• 35Q40
• 81Q30

Acknowledgments

The authors would like to express their gratitude to the referees for their valuable comments and suggestions which have improved the original paper.

Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2012R1A1A1004774).