Advanced search
1 file | 386.57 KB

Discrete Clifford analysis: the one-dimensional setting

Hendrik De Bie (UGent) , Hilde De Ridder (UGent) and Franciscus Sommen (UGent)
Author
Organization
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.
Keywords
discrete Fourier transform, Discrete Cliff ord analysis, discrete distribution theory, discrete delta functions

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 386.57 KB

Citation

Please use this url to cite or link to this publication:

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.
@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},
}

Altmetric
View in Altmetric
Web of Science
Times cited: