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Discrete Clifford analysis: the one-dimensional setting

Hendrik De Bie UGent, Hilde De Ridder UGent and Franciscus Sommen UGent (2012) COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. 57(7-8). p.903-920
abstract
In a higher dimensional setting, there are two major theories generalizing the theory of holomorphic functions in the complex plane, namely the theory of several complex variables and Cliff ord analysis. Discrete Cliff ord analysis is a discrete counterpart of the latter, studying the null functions of a discrete Dirac operator, which are called discrete monogenic functions. In this contribution, we give several new results in the one-dimensional case. We focus on the basic building blocks of discrete functions, namely discrete delta functions, in relation to the discrete vector variable operator . We introduce discrete distribution theory, in particular discrete delta distributions and defi ne a Fourier transform for discrete distributions. Finally, a comparison is made between discrete delta functions and distributions.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
discrete Fourier transform, Discrete Cliff ord analysis, discrete distribution theory, discrete delta functions
journal title
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
Complex Var. Elliptic Equ.
volume
57
issue
7-8
pages
903 - 920
Web of Science type
Article
Web of Science id
000306169500012
JCR category
MATHEMATICS
JCR impact factor
0.5 (2012)
JCR rank
173/296 (2012)
JCR quartile
3 (2012)
ISSN
1747-6933
DOI
10.1080/17476933.2011.636431
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
3032178
handle
http://hdl.handle.net/1854/LU-3032178
date created
2012-10-20 09:07:38
date last changed
2016-12-19 15:43:37
@article{3032178,
  abstract     = {In a higher dimensional setting, there are two major theories generalizing the theory of holomorphic functions in the complex plane, namely the theory of several complex variables and Cliff\unmatched{000b}ord analysis. Discrete Cliff\unmatched{000b}ord analysis is a discrete counterpart of the latter, studying the null functions of a discrete Dirac operator, which are called discrete monogenic functions. In this contribution, we give several new results in the one-dimensional case. We focus on the basic building blocks of discrete functions, namely discrete delta functions, in relation to the discrete vector variable operator \unmatched{0018}. We introduce discrete distribution theory, in particular discrete delta distributions \unmatched{000e}and defi\unmatched{000c}ne a Fourier transform for discrete distributions. Finally, a comparison is made between discrete delta functions and distributions.},
  author       = {De Bie, Hendrik and De Ridder, Hilde and Sommen, Franciscus},
  issn         = {1747-6933},
  journal      = {COMPLEX VARIABLES AND ELLIPTIC EQUATIONS},
  keyword      = {discrete Fourier transform,Discrete Cliff\unmatched{000b}ord analysis,discrete distribution theory,discrete delta functions},
  language     = {eng},
  number       = {7-8},
  pages        = {903--920},
  title        = {Discrete Clifford analysis: the one-dimensional setting},
  url          = {http://dx.doi.org/10.1080/17476933.2011.636431},
  volume       = {57},
  year         = {2012},
}

Chicago
De Bie, Hendrik, Hilde De Ridder, and Franciscus Sommen. 2012. “Discrete Clifford Analysis: The One-dimensional Setting.” Complex Variables and Elliptic Equations 57 (7-8): 903–920.
APA
De Bie, H., De Ridder, H., & Sommen, F. (2012). Discrete Clifford analysis: the one-dimensional setting. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 57(7-8), 903–920.
Vancouver
1.
De Bie H, De Ridder H, Sommen F. Discrete Clifford analysis: the one-dimensional setting. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. 2012;57(7-8):903–20.
MLA
De Bie, Hendrik, Hilde De Ridder, and Franciscus Sommen. “Discrete Clifford Analysis: The One-dimensional Setting.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 57.7-8 (2012): 903–920. Print.