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

作者：Bory Reyes J; Abreu Blaya R; Perez de la Rosa M A^*; Schneider B

来源：Complex Variables and Elliptic Equations, 2018, 63(11): 1509-1528.

DOI：10.1080/17476933.2017.1385067

• Hilbert operator
• hyperholomorphic functions
• singular integrals

We obtain some analogues of the Hilbert formulas on the unit circle for alpha-hyperholomorphic function theory in R-2 for a being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an alpha-hyperholomorphic function in the unit discwith the other pair of components and, hence, being analogous to the case of the theory of functions of one complex variable.

• 出版日期2018