Fourier transform in multiplicative analysis and its applications

This study focuses on multiplicative Fourier analysis. In the main results of our work, we first introduce multiplicative Riemann integrals. In this section, we construct multiplicative Riemann sums, prove the fundamental definitions and theorems, and establish the generalized integrals utilized in obtaining Fourier integrals. Subsequently, we present the complex form of the multiplicative Fourier series, which we then leverage to derive multiplicative Fourier integrals. Finally, building upon all these established definitions and theorems, we deduce the multiplicative Fourier transform and its inverse.