TY - JOUR
AU - Nashabeh, Luca
PY - 2024/08/05
Y2 - 2024/10/11
TI - The Peterâ€“Weyl theorem & harmonic analysis on S^n
JF - Columbia Journal of Undergraduate Mathematics
JA - CJUM
VL - 1
IS - 1
SE - Articles
DO -
UR - https://journals.library.columbia.edu/index.php/cjum/article/view/12910
SP -
AB - <p>For finite groups, the Artinâ€“Wedderburn theorem gives a precise decomposition of the algebra of all C-valued functions into matrix algebras. Specialized to the case of cyclic groups, this produces the classical discrete Fourier transform. In this paper, we endeavor to extend these techniques to compact topological groups, proving similar harmonic decompositions on S<sup>1</sup>, S<sup>2</sup>, and S<sup>3</sup>.</p>
ER -