Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters

Cristina Balderrama; Antonio Di Teodoro; Adrian Infante

doi:10.1007/s00006-013-0408-2

Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters

Cristina Balderrama
, Antonio Di Teodoro^*
, Adrian Infante

^*Corresponding author for this work

Central University of Venezuela
Universidad Simón Bolívar

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

17 Scopus citations

Abstract

In recent years, the integral representation problems have been studied in many context and generalities. For example, for the monogenic and meta functions in some Clifford type algebras, see [10, 11].In this paper we construct a Cauchy-Pompeiu type formula for meta-monogenic operator of order n, (D-λ)ⁿ, λ ∈ ℝ, and its conjugate (D̄-λ)ⁿ in a Clifford algebra depending on parameters A_n(2, α_j, γ_ij). Using these explicit representation formula of Cauchy-Pompeiu type we will show some applications.

Original language	English
Pages (from-to)	793-813
Number of pages	21
Journal	Advances in Applied Clifford Algebras
Volume	23
Issue number	4
DOIs	https://doi.org/10.1007/s00006-013-0408-2
State	Published - Dec 2013
Externally published	Yes

Keywords

Clifford type algebras
Meta-monogenic function
fundamental solutions
high order Cauchy-Pompeiu integral formula

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10.1007/s00006-013-0408-2

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title = "Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters",

abstract = "In recent years, the integral representation problems have been studied in many context and generalities. For example, for the monogenic and meta functions in some Clifford type algebras, see [10, 11].In this paper we construct a Cauchy-Pompeiu type formula for meta-monogenic operator of order n, (D-λ)n, λ ∈ ℝ, and its conjugate ({\=D}-λ)n in a Clifford algebra depending on parameters An(2, αj, γij). Using these explicit representation formula of Cauchy-Pompeiu type we will show some applications.",

keywords = "Clifford type algebras, Meta-monogenic function, fundamental solutions, high order Cauchy-Pompeiu integral formula",

author = "Cristina Balderrama and \{Di Teodoro\}, Antonio and Adrian Infante",

note = "Funding Information: ∗Corresponding author This work was completed with the support of Universidad Central de Venezuela and Uni-versidad Sim{\'o}n Bol{\'i}var.",

year = "2013",

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TY - JOUR

T1 - Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters

AU - Balderrama, Cristina

AU - Di Teodoro, Antonio

AU - Infante, Adrian

N1 - Funding Information: ∗Corresponding author This work was completed with the support of Universidad Central de Venezuela and Uni-versidad Simón Bolívar.

PY - 2013/12

Y1 - 2013/12

N2 - In recent years, the integral representation problems have been studied in many context and generalities. For example, for the monogenic and meta functions in some Clifford type algebras, see [10, 11].In this paper we construct a Cauchy-Pompeiu type formula for meta-monogenic operator of order n, (D-λ)n, λ ∈ ℝ, and its conjugate (D̄-λ)n in a Clifford algebra depending on parameters An(2, αj, γij). Using these explicit representation formula of Cauchy-Pompeiu type we will show some applications.

AB - In recent years, the integral representation problems have been studied in many context and generalities. For example, for the monogenic and meta functions in some Clifford type algebras, see [10, 11].In this paper we construct a Cauchy-Pompeiu type formula for meta-monogenic operator of order n, (D-λ)n, λ ∈ ℝ, and its conjugate (D̄-λ)n in a Clifford algebra depending on parameters An(2, αj, γij). Using these explicit representation formula of Cauchy-Pompeiu type we will show some applications.

KW - Clifford type algebras

KW - Meta-monogenic function

KW - fundamental solutions

KW - high order Cauchy-Pompeiu integral formula

UR - https://www.scopus.com/pages/publications/84887298505

U2 - 10.1007/s00006-013-0408-2

DO - 10.1007/s00006-013-0408-2

M3 - Artículo

AN - SCOPUS:84887298505

SN - 0188-7009

VL - 23

SP - 793

EP - 813

JO - Advances in Applied Clifford Algebras

JF - Advances in Applied Clifford Algebras

IS - 4

ER -

Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters

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Keywords

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