On the generalized Hartley-Hilbert and Fourier-Hilbert transforms

On the generalized Hartley and Hartley-Hilbert transformations

*Correspondence: [email protected] 2Department of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia (UPM), Serdang, Selangor 43400, Malaysia Full list of author information is available at the end of the article Abstract In this paper, we extend Hartley and Hartley-Hilbert transformations (HT and HHT, respectively) to a certain space of tempered distribution...

Generalized multidimensional Hilbert transforms in Clifford analysis

During the last fifty years, Clifford analysis has gradually developed to a comprehensive theory offering a direct, elegant, and powerful generalization to higher dimension of the theory of holomorphic functions in the complex plane. In its most simple but still useful setting, flat m-dimensional Euclidean space, Clifford analysis focusses on the so-called monogenic functions, that is, null sol...

Two-dimensional Hilbert Transforms'

Discrete Fractional Hartley and Fourier Transforms

This paper is concerned with the definitions of the discrete fractional Hartley transform (DFRHT) and the discrete fractional Fourier transform (DFRFT). First, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated. Then, the results of the eigendecompositions of the transform matrices are used to define DFRHT and DFRFT. Also, an important relat...

Generalized Frames in Hilbert Spaces