Seminarium KMMF "Teoria Dwoistości"

The Clifford analysis extends the theory of complex variable functions to high-dimensional spaces, which mainly studies the properties of functions defined on R^n with values in Clifford algebra Cl{0,n}. More precisely, the quaternion algebra H is isomorphic to the Clifford algebra Cl_{0,2}.I will present the differential formulas and the uncertainty principles of the quaternion fractional Fourier transform, the Clifford-Fourier transform, and the fractional Clifford-Fourier transform.