Some shaper uncertainty principles for multivector-valued functions

Abstract

The Heisenberg uncertainty principle and the uncertainty principle for self-adjoint operators have been known and applied for decades. In this paper, in the framework of Clifford algebra, we establish a stronger Heisenberg–Pauli–Wely type uncertainty principle for the Fourier transform of multivector-valued functions, which generalizes the recent results about uncertainty principles of Clifford–Fourier transform. At the end, we consider another stronger uncertainty principle for the Dunkl transform of multivector-valued functions.