The classical theory of the Fourier transform, initially designed to analyze periodic functions on the real line, has seen remarkable growth thanks to its extension to more complex algebraic structures. Fourier analysis on groups, particularly on topological groups, is now positioned as a fundamental pillar in the study of harmonic and spectral phenomena beyond usual … Read more
The analysis of Lie groups stands out as a fascinating discipline blending algebra, geometry, and analysis. Since its origins, it has shed light on the fine understanding of continuous symmetries that govern both quantum mechanics and modern differential geometry. In 2025, this mathematical field explores with particular dynamism the interactions between the representations of compact … Read more
Lie groups represent a cornerstone in understanding continuous symmetries that shape both pure geometry and advanced physical theories. Their study allows one to grasp the deep nature of continuous transformations that preserve certain differentiable structures and offers a bridge between abstract mathematics and its concrete applications in physics and geometry. This field of research, heir … Read more