Duality Property of Two-Sided Quaternion Fourier Transform

Abstract

An alternative proof of scalar Parseval's formula with respect to the two-sided quaternion Fourier transform is presented. It is shown that the inverse of the two-sided quaternion Fourier transform is continuous and bounded on R 2. The duality property of the two-sided quaternion Fourier transform is established. The alternative form of the Hausdorff-Young inequality associated with the two-sided quaternion Fourier transform is expressed. AMS Subject Classification: 11R52, 42A38, 15A66