A remark on the inversion of the magnification bias in the quasar-galaxy associations

TL;DR

This paper introduces a simple Mellin transform-based method to invert gravitational lensing effects and recover the true quasar luminosity function from observed data, confirming previous findings.

Contribution

It proposes a novel, intuitive inversion technique for magnification bias using Mellin transforms, simplifying the process compared to existing complex methods.

Findings

Successfully recovers the intrinsic quasar luminosity function

Validates previous results in the literature

Provides a straightforward alternative method for lensing analysis

Abstract

We present an alternative but intuitive method of obtaining the true or intrinsic quasar luminosity function through the observed one in the framework of gravitational lensing. Such a so-called inversion of the magnification bias can be straightforwardly performed by means of the Mellin transformation instead of other complex methods. Application of our approach to the well-known form of the observed quasar luminosity function identifies the previous results in literature.