Computing some Principal Value integrals without Residues and Applications on Hilbert Transform and Fourier Transform
Year: 2024
Type: preprint
Abstract: This article proposes a new approach in the treatment of the Hilbert transform and some cases of the Fourier transform whose improper integrals are principal values. This approach may be useful for teaching these issues to undergraduate engineering students. Traditional literature of Complex Analysis deals with these transformation integrals with the Cauchy-Goursat theorem and the residues calculation technique. In this new approach, instead of residues, we use an intuitive result about complex line integrals of continuous complex functions that resembles the delta of Dirac.
Source: arXiv (Cornell University)
Author: Arpasi, Jorge Pedraza
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393968877