Hypercomplex fourier and laplace transforms II

Abstract

In this paper the exponential function introduced in [14] and the Cauchy kernel introduced in [7] are used to study new kinds of Fourier, Laplace, Cauchy and Hilbert transforms of A valued L ₂-functions in , where A is a Clifford algebra. In this way the corresponding theory in the complex plane (see [1], [2]) is generalized in the hypercomplex setting to several dimensions.

AMS (MOS):

• 30635
• 42B10
• 44A10
• 44A15
• 46F20

^∗Research Assistant of the National Fund for Scientific Research (Belgium).

^∗Research Assistant of the National Fund for Scientific Research (Belgium).

Notes

^∗Research Assistant of the National Fund for Scientific Research (Belgium).