Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals

M. E. Luna-Elizarrarás, M. A. Macías-Cedeño, M. Shapiro

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

© 2008 Birkhäuser Verlag Basel/Switzerland. We introduce the notion of the derivative as the limit of a quotient where the numerator and the denominator represent a kind of the "increments" of a function and of the independent variable respectively. The directional derivative is introduced where a direction means a hyperplane in Rm+1 for a Clifford algebra Cl0,m. The latter applies for obtaining a formula showing how to exchange the integral sign and the hyperderivative of the Cliffordian Cauchy-type integral as a hyperholomorphic function.
Original languageAmerican English
Title of host publicationHyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals
Pages221-234
Number of pages197
ISBN (Electronic)9783764398927
StatePublished - 1 Jan 2009
EventTrends in Mathematics -
Duration: 1 Jan 2009 → …

Publication series

NameTrends in Mathematics
Volume48
ISSN (Print)2297-0215

Conference

ConferenceTrends in Mathematics
Period1/01/09 → …

Fingerprint

Cauchy-type Integral
Clifford Analysis
Numerator
Directional derivative
Clifford Algebra
Denominator
Hyperplane
Increment
Quotient
Derivative

Cite this

Luna-Elizarrarás, M. E., Macías-Cedeño, M. A., & Shapiro, M. (2009). Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. In Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals (pp. 221-234). (Trends in Mathematics; Vol. 48).
Luna-Elizarrarás, M. E. ; Macías-Cedeño, M. A. ; Shapiro, M. / Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. 2009. pp. 221-234 (Trends in Mathematics).
@inproceedings{a44b3badee1b46c68b093bc2277047ea,
title = "Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals",
abstract = "{\circledC} 2008 Birkh{\"a}user Verlag Basel/Switzerland. We introduce the notion of the derivative as the limit of a quotient where the numerator and the denominator represent a kind of the {"}increments{"} of a function and of the independent variable respectively. The directional derivative is introduced where a direction means a hyperplane in Rm+1 for a Clifford algebra Cl0,m. The latter applies for obtaining a formula showing how to exchange the integral sign and the hyperderivative of the Cliffordian Cauchy-type integral as a hyperholomorphic function.",
author = "Luna-Elizarrar{\'a}s, {M. E.} and Mac{\'i}as-Cede{\~n}o, {M. A.} and M. Shapiro",
year = "2009",
month = "1",
day = "1",
language = "American English",
isbn = "9783764398927",
series = "Trends in Mathematics",
pages = "221--234",
booktitle = "Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals",

}

Luna-Elizarrarás, ME, Macías-Cedeño, MA & Shapiro, M 2009, Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. in Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. Trends in Mathematics, vol. 48, pp. 221-234, Trends in Mathematics, 1/01/09.

Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. / Luna-Elizarrarás, M. E.; Macías-Cedeño, M. A.; Shapiro, M.

Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. 2009. p. 221-234 (Trends in Mathematics; Vol. 48).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals

AU - Luna-Elizarrarás, M. E.

AU - Macías-Cedeño, M. A.

AU - Shapiro, M.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - © 2008 Birkhäuser Verlag Basel/Switzerland. We introduce the notion of the derivative as the limit of a quotient where the numerator and the denominator represent a kind of the "increments" of a function and of the independent variable respectively. The directional derivative is introduced where a direction means a hyperplane in Rm+1 for a Clifford algebra Cl0,m. The latter applies for obtaining a formula showing how to exchange the integral sign and the hyperderivative of the Cliffordian Cauchy-type integral as a hyperholomorphic function.

AB - © 2008 Birkhäuser Verlag Basel/Switzerland. We introduce the notion of the derivative as the limit of a quotient where the numerator and the denominator represent a kind of the "increments" of a function and of the independent variable respectively. The directional derivative is introduced where a direction means a hyperplane in Rm+1 for a Clifford algebra Cl0,m. The latter applies for obtaining a formula showing how to exchange the integral sign and the hyperderivative of the Cliffordian Cauchy-type integral as a hyperholomorphic function.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84961375148&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84961375148&origin=inward

M3 - Conference contribution

SN - 9783764398927

T3 - Trends in Mathematics

SP - 221

EP - 234

BT - Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals

ER -

Luna-Elizarrarás ME, Macías-Cedeño MA, Shapiro M. Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. In Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals. 2009. p. 221-234. (Trends in Mathematics).