The application of the calculus of divergent integrals to Fourier transforms of exponential type functions

  • Jan Carlo Lubao Lima National Institute of Physics, University of the Philippines Diliman
  • John Paul A Besagas National Institute of Physics, University of the Philippines Diliman
  • Eric A Galapon National Institute of Physics, University of the Philippines Diliman

Abstract

We consider evaluating the Fourier transform of products of entire and exponential type functions by expressing the Fourier integral in terms of a finite sum of divergent integrals and assigning the divergent integrals values equal to their lower boundary values (LBVs). The method leads to the correct Fourier transform. Moreover, we show from the obtained Fourier transforms that the type of the product of the entire and exponential type functions is equal to the sum of their individual types. Finally, we demonstrate the application of this work in the Fourier integrals arising in environment-free decoherence model.

Published
2018-05-21
How to Cite
[1]
J. C. Lima, J. P. Besagas, and E. Galapon. The application of the calculus of divergent integrals to Fourier transforms of exponential type functions, Proceedings of the Samahang Pisika ng Pilipinas 36, SPP-2018-PC-06 (2018). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2018-PC-06.
Section
Poster Session C (Mathematical Physics, Optics, and Interdisciplinary Topics)