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A matrix Hilbert transform in Hermitean Clifford analysis. (English) Zbl 1148.44004

The authors introduce a new Hermitean Hilbert transform, arising as part of the non-tangential boundary limits of that Hermitean Cauchy integral. The resulting matrix operator is shown to satisfy property adapted analogues of the characteristic properties of the Hilbert transform in classical analysis and orthogonal clifford analysis.

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
30G30 Other generalizations of analytic functions (including abstract-valued functions)
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