Real Paley-Wiener theorems for the Clifford Fourier transform

Associated with the Dirac operator and partial derivatives, this paper establishes some real Paley-Wiener type theorems to characterize the Clifford-valued functions whose Clifford Fourier transform (CFT) has compact support. Based on the Riemann-Lebesgue theorem for the CFT, the Boas theorem is provided to describe the CFT of Clifford-valued functions that vanish on a neighborhood of the origin.