Undergrad Invert an integral equation to find this unknown

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SUMMARY

The discussion centers on the process of inverting an integral equation using inverse Fourier transforms, specifically referencing equation (3.71). Participants emphasize the importance of understanding the conventions in physics, such as the placement of measures in front of the integrand and the factors of π. The clarity of the responses provided is noted as beneficial for grasping these concepts.

PREREQUISITES
  • Understanding of Fourier transforms
  • Familiarity with integral equations
  • Knowledge of mathematical conventions in physics
  • Basic grasp of π and its significance in equations
NEXT STEPS
  • Study the properties of inverse Fourier transforms
  • Explore integral equation techniques in applied mathematics
  • Review mathematical conventions used in physics
  • Investigate the role of π in various mathematical contexts
USEFUL FOR

Mathematicians, physicists, and students involved in advanced mathematics or theoretical physics who are looking to deepen their understanding of integral equations and Fourier analysis.

Replusz
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TL;DR
I don't quite understand the steps taken to get to the second line (3.71->3.72):
(http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf)
1586804336609.png
 
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Apart from the insane habit in physics to write the measure in front of the integrand (:wink:) and other conventions related to factors of ##\pi##, this follows from taking inverse Fourier transforms on both sides of (3.71).
 
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Thank you for your quick and perfectly clear reply! :)
 
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