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

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	1509-1528
Number of pages	20
Journal	Complex Variables and Elliptic Equations
Volume	63
Issue number	11
DOIs	https://doi.org/10.1080/17476933.2017.1385067
State	Published - 2 Nov 2018

Keywords

30G35
42B20
44A15
Hilbert operator
hyperholomorphic functions
singular integrals

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10.1080/17476933.2017.1385067

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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.",

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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.

KW - 30G35

KW - 42B20

KW - 44A15

KW - Hilbert operator

KW - hyperholomorphic functions

KW - singular integrals

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DO - 10.1080/17476933.2017.1385067

M3 - Artículo

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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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Keywords

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