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General Integral Formulas for k-hyper-mono-genic Functions

Tutkimustuotosvertaisarvioitu

Standard

General Integral Formulas for k-hyper-mono-genic Functions. / Eriksson, Sirkka-Liisa; Orelma, Heikki.

julkaisussa: Advances in Applied Clifford Algebras, Vuosikerta 27, Nro 1, 2017, s. 99-110.

Tutkimustuotosvertaisarvioitu

Harvard

Eriksson, S-L & Orelma, H 2017, 'General Integral Formulas for k-hyper-mono-genic Functions', Advances in Applied Clifford Algebras, Vuosikerta. 27, Nro 1, Sivut 99-110. https://doi.org/10.1007/s00006-015-0629-7

APA

Eriksson, S-L., & Orelma, H. (2017). General Integral Formulas for k-hyper-mono-genic Functions. Advances in Applied Clifford Algebras, 27(1), 99-110. https://doi.org/10.1007/s00006-015-0629-7

Vancouver

Eriksson S-L, Orelma H. General Integral Formulas for k-hyper-mono-genic Functions. Advances in Applied Clifford Algebras. 2017;27(1):99-110. https://doi.org/10.1007/s00006-015-0629-7

Author

Eriksson, Sirkka-Liisa ; Orelma, Heikki. / General Integral Formulas for k-hyper-mono-genic Functions. Julkaisussa: Advances in Applied Clifford Algebras. 2017 ; Vuosikerta 27, Nro 1. Sivut 99-110.

Bibtex - Lataa

@article{8c4e5ef2db6e4c19ac1c6a73675f821f,
title = "General Integral Formulas for k-hyper-mono-genic Functions",
abstract = "We are studying a function theory of k-hypermonogenic functions connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric k2=xn2k1-n(dx02+⋯+dxn2)in the upper half space R+n+1={(x0,…,xn)|xi∈R,xn>0}. The function theory based on this metric is important, since in case k= n- 1 , the metric is the hyperbolic metric of the Poincar{\'e} upper half space and Leutwiler noticed that the power function xm(m∈N0), calculated using Clifford algebras, is a conjugate gradient of a hyperbolic harmonic function. We find a fundamental k-hyperbolic harmonic function. Using this function we are able to find kernels and integral formulas for k-hypermonogenic functions. Earlier these results have been verified for hypermonogenic functions (k= n- 1) and for k-hyperbolic harmonic functions in odd dimensional spaces.",
author = "Sirkka-Liisa Eriksson and Heikki Orelma",
year = "2017",
doi = "10.1007/s00006-015-0629-7",
language = "English",
volume = "27",
pages = "99--110",
journal = "Advances in Applied Clifford Algebras",
issn = "0188-7009",
publisher = "Springer Verlag",
number = "1",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - General Integral Formulas for k-hyper-mono-genic Functions

AU - Eriksson, Sirkka-Liisa

AU - Orelma, Heikki

PY - 2017

Y1 - 2017

N2 - We are studying a function theory of k-hypermonogenic functions connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric k2=xn2k1-n(dx02+⋯+dxn2)in the upper half space R+n+1={(x0,…,xn)|xi∈R,xn>0}. The function theory based on this metric is important, since in case k= n- 1 , the metric is the hyperbolic metric of the Poincaré upper half space and Leutwiler noticed that the power function xm(m∈N0), calculated using Clifford algebras, is a conjugate gradient of a hyperbolic harmonic function. We find a fundamental k-hyperbolic harmonic function. Using this function we are able to find kernels and integral formulas for k-hypermonogenic functions. Earlier these results have been verified for hypermonogenic functions (k= n- 1) and for k-hyperbolic harmonic functions in odd dimensional spaces.

AB - We are studying a function theory of k-hypermonogenic functions connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric k2=xn2k1-n(dx02+⋯+dxn2)in the upper half space R+n+1={(x0,…,xn)|xi∈R,xn>0}. The function theory based on this metric is important, since in case k= n- 1 , the metric is the hyperbolic metric of the Poincaré upper half space and Leutwiler noticed that the power function xm(m∈N0), calculated using Clifford algebras, is a conjugate gradient of a hyperbolic harmonic function. We find a fundamental k-hyperbolic harmonic function. Using this function we are able to find kernels and integral formulas for k-hypermonogenic functions. Earlier these results have been verified for hypermonogenic functions (k= n- 1) and for k-hyperbolic harmonic functions in odd dimensional spaces.

U2 - 10.1007/s00006-015-0629-7

DO - 10.1007/s00006-015-0629-7

M3 - Article

VL - 27

SP - 99

EP - 110

JO - Advances in Applied Clifford Algebras

JF - Advances in Applied Clifford Algebras

SN - 0188-7009

IS - 1

ER -