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

J. Bory Reyes; R. Abreu Blaya; M. A. Pérez-de la Rosa; B. Schneider

doi:10.1080/17476933.2017.1385067

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

J. Bory Reyes, R. Abreu Blaya, M. A. Pérez-de la Rosa, B. Schneider

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

2 Citas (Scopus)

Resumen

We obtain some analogues of the Hilbert formulas on the unit circle for α-hyperholomorphic function theory in R² for α being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an α-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.

Idioma original	Inglés
Páginas (desde-hasta)	1509-1528
Número de páginas	20
Publicación	Complex Variables and Elliptic Equations
Volumen	63
N.º	11
DOI	https://doi.org/10.1080/17476933.2017.1385067
Estado	Publicada - 2 nov. 2018

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abstract = "We obtain some analogues of the Hilbert formulas on the unit circle for α-hyperholomorphic function theory in R2 for α being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an α-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.",

keywords = "30G35, 42B20, 44A15, Hilbert operator, hyperholomorphic functions, singular integrals",

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AU - Bory Reyes, J.

AU - Abreu Blaya, R.

AU - Pérez-de la Rosa, M. A.

AU - Schneider, B.

PY - 2018/11/2

Y1 - 2018/11/2

N2 - We obtain some analogues of the Hilbert formulas on the unit circle for α-hyperholomorphic function theory in R2 for α being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an α-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.

AB - We obtain some analogues of the Hilbert formulas on the unit circle for α-hyperholomorphic function theory in R2 for α being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an α-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.

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KW - 42B20

KW - 44A15

KW - Hilbert operator

KW - hyperholomorphic functions

KW - singular integrals

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DO - 10.1080/17476933.2017.1385067

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SP - 1509

EP - 1528

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 11

ER -

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

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