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On k-Hypermonogenic Functions and Their Mean Value Properties

Tutkimustuotosvertaisarvioitu

Standard

On k-Hypermonogenic Functions and Their Mean Value Properties. / Eriksson, Sirkka-Liisa; Orelma, Heikki.

julkaisussa: Complex Analysis and Operator Theory, Vuosikerta 10, Nro 2, 2016, s. 311-325.

Tutkimustuotosvertaisarvioitu

Harvard

Eriksson, S-L & Orelma, H 2016, 'On k-Hypermonogenic Functions and Their Mean Value Properties', Complex Analysis and Operator Theory, Vuosikerta. 10, Nro 2, Sivut 311-325. https://doi.org/10.1007/s11785-015-0445-z

APA

Eriksson, S-L., & Orelma, H. (2016). On k-Hypermonogenic Functions and Their Mean Value Properties. Complex Analysis and Operator Theory, 10(2), 311-325. https://doi.org/10.1007/s11785-015-0445-z

Vancouver

Author

Eriksson, Sirkka-Liisa ; Orelma, Heikki. / On k-Hypermonogenic Functions and Their Mean Value Properties. Julkaisussa: Complex Analysis and Operator Theory. 2016 ; Vuosikerta 10, Nro 2. Sivut 311-325.

Bibtex - Lataa

@article{c6a5cf4fa61c4ece8484b21ac9bcb3ca,
title = "On k-Hypermonogenic Functions and Their Mean Value Properties",
abstract = "We study a hyperbolic version of holomorphic functions to higher dimensions. In this frame work, a generalization of holomorphic functions are called (Formula presented.)-hypermonogenic functions. These functions are depending on several real variables and their values are in a Clifford algebra. They are defined in terms of hyperbolic Dirac operators. They are connected to harmonic functions with respect to the Riemannian metric (Formula presented.) in the same way as the usual harmonic function to holomorphic functions. We present the mean value property for (Formula presented.)-hypermonogenic functions and related results. Earlier the mean value properties has been proved for hypermonogenic functions. The key tools are the invariance properties of the hyperbolic metric.",
keywords = "Dirac operator, Hyperbolic metric, Hypermonogenic, Monogenic",
author = "Sirkka-Liisa Eriksson and Heikki Orelma",
year = "2016",
doi = "10.1007/s11785-015-0445-z",
language = "English",
volume = "10",
pages = "311--325",
journal = "Complex Analysis and Operator Theory",
issn = "1661-8254",
publisher = "Springer Verlag",
number = "2",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - On k-Hypermonogenic Functions and Their Mean Value Properties

AU - Eriksson, Sirkka-Liisa

AU - Orelma, Heikki

PY - 2016

Y1 - 2016

N2 - We study a hyperbolic version of holomorphic functions to higher dimensions. In this frame work, a generalization of holomorphic functions are called (Formula presented.)-hypermonogenic functions. These functions are depending on several real variables and their values are in a Clifford algebra. They are defined in terms of hyperbolic Dirac operators. They are connected to harmonic functions with respect to the Riemannian metric (Formula presented.) in the same way as the usual harmonic function to holomorphic functions. We present the mean value property for (Formula presented.)-hypermonogenic functions and related results. Earlier the mean value properties has been proved for hypermonogenic functions. The key tools are the invariance properties of the hyperbolic metric.

AB - We study a hyperbolic version of holomorphic functions to higher dimensions. In this frame work, a generalization of holomorphic functions are called (Formula presented.)-hypermonogenic functions. These functions are depending on several real variables and their values are in a Clifford algebra. They are defined in terms of hyperbolic Dirac operators. They are connected to harmonic functions with respect to the Riemannian metric (Formula presented.) in the same way as the usual harmonic function to holomorphic functions. We present the mean value property for (Formula presented.)-hypermonogenic functions and related results. Earlier the mean value properties has been proved for hypermonogenic functions. The key tools are the invariance properties of the hyperbolic metric.

KW - Dirac operator

KW - Hyperbolic metric

KW - Hypermonogenic

KW - Monogenic

U2 - 10.1007/s11785-015-0445-z

DO - 10.1007/s11785-015-0445-z

M3 - Article

VL - 10

SP - 311

EP - 325

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

SN - 1661-8254

IS - 2

ER -