On the Hilbert formulas on the unit circle for α-hyperholomorphic function theory

We obtain some analogues of the Hilbert formulas on the unit circle for -hyperholomorphic function theory in for being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an -hyperholomorphic function in the unit disc with the other pair of compo...

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Bibliographic Details
Published in:Complex variables and elliptic equations 2018-11, Vol.63 (11), p.1509-1528
Main Authors: Bory Reyes, J., Abreu Blaya, R., Pérez-de la Rosa, M. A., Schneider, B.
Format: Article
Language:English
Subjects:
Hilbert operator
hyperholomorphic functions
singular integrals
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Summary:We obtain some analogues of the Hilbert formulas on the unit circle for -hyperholomorphic function theory in for being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an -hyperholomorphic function in the unit disc with the other pair of components and, hence, being analogous to the case of the theory of functions of one complex variable.
ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2017.1385067