Some applications of the convolution theorem of the hilbert transform

Abstract

For the Hilbert transform

a new proof of the convolution formula is given. This convolution formula is then applied to calculate some Cauchy integrals and to solve a nonlinear singular integral equation

Keywords:

• Hilbert transform
• convolution
• nonlinear singular integral equation

MSC(1991):

• 44A15
• 44A35

^*The work of this author was supported by the Alexander von Humboldt Foundation and the Kuwait University research grant

^*The work of this author was supported by the Alexander von Humboldt Foundation and the Kuwait University research grant

Notes

^*The work of this author was supported by the Alexander von Humboldt Foundation and the Kuwait University research grant