Cauchy-Pompeiu type integral formula for multi-harmonic functions

Johan Ceballos; Mariana Ceballos; Antonio Di Teodoro; Daniel González; Diego Ochoa-Tocachi

Cauchy-Pompeiu type integral formula for multi-harmonic functions

Johan Ceballos^*
, Mariana Ceballos
, Antonio Di Teodoro
, Daniel González
, Diego Ochoa-Tocachi

^*Corresponding author for this work

Matemáticas

Centro de Bioinformática y Biología Computacional de Colombia - BIOS
Universidad EAFIT
Universidad de las Americas - Ecuador
ATUK Consultoría Estratégica

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

Abstract

In the present work, we use a multi-dimensional Clifford type algebra to construct a Cauchy-Pompeiu type integral formula for multi-harmonic functions (also called separately-harmonic functions), which are defined in the domain of R^mi+1 X R= X · · · X R^m-+1. For this purpose, we use the fundamental solution for some second order elliptic operators constructed using the non-Euclidean distance. Finally, we show how we can obtain a Cauchy type formula using iterations.

Original language	English
Pages (from-to)	75-102
Number of pages	28
Journal	Bulletin of Computational Applied Mathematics
Volume	11
Issue number	1
State	Published - 2023

Keywords

Cauchy-Pompeiu type integral
Clifford-type algebra
fundamental solution
harmonic functions
multi-dimensional Clifford algebra
multi-harmonic functions

Cite this

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title = "Cauchy-Pompeiu type integral formula for multi-harmonic functions",

abstract = "In the present work, we use a multi-dimensional Clifford type algebra to construct a Cauchy-Pompeiu type integral formula for multi-harmonic functions (also called separately-harmonic functions), which are defined in the domain of Rmi+1 X R= X · · · X Rm-+1. For this purpose, we use the fundamental solution for some second order elliptic operators constructed using the non-Euclidean distance. Finally, we show how we can obtain a Cauchy type formula using iterations.",

keywords = "Cauchy-Pompeiu type integral, Clifford-type algebra, fundamental solution, harmonic functions, multi-dimensional Clifford algebra, multi-harmonic functions",

author = "Johan Ceballos and Mariana Ceballos and \{Di Teodoro\}, Antonio and Daniel Gonz{\'a}lez and Diego Ochoa-Tocachi",

year = "2023",

language = "Ingl{\'e}s",

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T1 - Cauchy-Pompeiu type integral formula for multi-harmonic functions

AU - Ceballos, Johan

AU - Ceballos, Mariana

AU - Di Teodoro, Antonio

AU - González, Daniel

AU - Ochoa-Tocachi, Diego

PY - 2023

Y1 - 2023

N2 - In the present work, we use a multi-dimensional Clifford type algebra to construct a Cauchy-Pompeiu type integral formula for multi-harmonic functions (also called separately-harmonic functions), which are defined in the domain of Rmi+1 X R= X · · · X Rm-+1. For this purpose, we use the fundamental solution for some second order elliptic operators constructed using the non-Euclidean distance. Finally, we show how we can obtain a Cauchy type formula using iterations.

AB - In the present work, we use a multi-dimensional Clifford type algebra to construct a Cauchy-Pompeiu type integral formula for multi-harmonic functions (also called separately-harmonic functions), which are defined in the domain of Rmi+1 X R= X · · · X Rm-+1. For this purpose, we use the fundamental solution for some second order elliptic operators constructed using the non-Euclidean distance. Finally, we show how we can obtain a Cauchy type formula using iterations.

KW - Cauchy-Pompeiu type integral

KW - Clifford-type algebra

KW - fundamental solution

KW - harmonic functions

KW - multi-dimensional Clifford algebra

KW - multi-harmonic functions

UR - https://www.scopus.com/pages/publications/85187192081

M3 - Artículo

AN - SCOPUS:85187192081

SN - 2244-8659

VL - 11

SP - 75

EP - 102

JO - Bulletin of Computational Applied Mathematics

JF - Bulletin of Computational Applied Mathematics

IS - 1

ER -

Cauchy-Pompeiu type integral formula for multi-harmonic functions

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Keywords

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