Some Useful Results Associated with Right-Sided Quaternion Fourier Transform

Abstract

The uncertainty principles can be regarded as generalization of the uncertainty principles on complex Hilbert space. By applying the linear operators, it is shown that the right-sided quaternion Fourier transform is a unitary operator. The duality property of the right-sided quaternion Fourier transform which enables us to express the alternative form of the Hausdorff-Young inequality associated with the right-sided quaternion Fourier transform is presented. AMS Subject Classification: 11R52, 42A38, 15A66