4 papers · 1 filter
Characterizing the Fourier transform by its properties
Mateusz Krukowski
It is common knowledge that the Fourier transform enjoys the convolution property, i.e., it turns convolution in the time domain into multiplication in the frequency domain. It is…
Integral transforms characterized by convolution
Mateusz Krukowski
Inspired by Jaming's characterization of the Fourier transform on specific groups via the convolution property, we provide a novel approach which characterizes the Fourier transfor…
From Schwartz space to Mellin transform
Mateusz Krukowski
The primary motivation behind this paper is an attempt to provide a thorough explanation of how the Mellin transform arises naturally in a process akin to the construction of the c…
Short note on Smithson's paper concerning Arzelà-Ascoli theorem for multifunctions
Mateusz Krukowski
As indicated in the title, this paper was inspired by Smithson's work on Arzelà-Ascoli theorem. Up to this point, the author's interest in the topic has led him to generalize Arzel…