53
Views
12
CrossRef citations to date
0
Altmetric
Original Article

A Basic Framework for Discrete Clifford Analysis

, &
Pages 385-395 | Published online: 30 Jan 2011

  • I. Benjamini and L. Lovász. "Harmonic and Analytic Functions on Graphs." J. Geom. 76 (2002), 3–15.
  • F. Brackx, R. Delanghe, and F. Sommen. Clifford Analysis . Boston: Pitman, 1982.
  • F. Brackx, J. Bureš, H. De Schepper, D. Eelbode, F. Sommen, and V. Souček. "Fundaments of Hermitean Clifford Analysis. Part I: Complex Structure." Comp. Anal. Oper. Theory 1:3 (2007), 341–365.
  • F. Brackx, J. Bureš, H. De Schepper, D. Eelbode, F. Sommen, and V. Souček. "Fundaments of Hermitean Clifford Analysis. Part II: Splitting of h -Monogenic Equations." Comp. Var. Elliptic Equ. 52:10–11 (2007), 1063–1079.
  • F. Brackx, H. De Schepper, F. Sommen, and L. Van de Voorde. "Discrete Clifford Analysis: A Germ of Function Theory." In Hypercomplex Analysis, edited by I. Sabadini, M. Shapiro, and F. Sommen, pp. 37–54, Trends in Mathematics. Boston: Birkhüuser, 2009.
  • R. Delanghe, F. Sommen, and V. Souček. Clifford Algebra and Spinor-Valued Functions . Dordrecht: Kluwer Academic Publishers, 1992.
  • R. Duffin. "Basic Properties of Discrete Analytic Functions." Duke Math. J. 23 (1956), 335–363.
  • N. Faustino and U. Kaehler. "Fischer Decomposition for Difference Dirac Operators." Adv. Appl. Clifford Algebras 17:1 (2007), 37–58.
  • N. Faustino and U. Kaehler. "On a Correspondence Principle between Discrete Differential Forms, Graph Structure and Multi-vector Calculus on Symmetric Lattices." arXiv:0712.1004, 2007.
  • N. Faustino, K. Guerlebeck, A. Hommel, and U. Kaehler. "Difference Potentials for the Navier– Stokes Equations in Unbounded Domains." J. Difference Equ. Appl. 12:6 (2006), 577–595.
  • N. Faustino, U. Kaehler, and F. Sommen. "Discrete Dirac Operators in Clifford Analysis." Adv. Appl. Clifford Algebras 17:3 (2007), 451–467.
  • J. Ferrand. "Fonctions préharmoniques et fonctions préholomorphes." Bull. Sci. Math. 68 (1944), 152– 180.
  • J. Gilbert and M. Murray. Clifford Algebras and Dirac Operators in Harmonic Analysis . Cambridge: Cambridge University Press, 1991.
  • K. Guerlebeck and A. Hommel. "On Finite Difference Dirac Operators and Their Fundamental Aolutions." Adv. Appl. Clifford Algebras 11:S2 (2001), 89–106.
  • K. Guerlebeck and A. Hommel. "On Finite Difference Potentials and Their Applications in a Discrete Function Theory." Math. Methods Appl. Sci. 25:16–18 (2002), 1563–1576.
  • K. Guerlebeck and W. Sproessig. Quaternionic Analysis and Elliptic Boundary Value Problems, International Series of Numerical Mathematics 89. Basel: Birkhäuser, 1990.
  • K. Guerlebeck and W. Sproessig. Quaternionic and Clifford Calculus for Engineers and Physicists . Chichester: John Wiley & Sons, 1997.
  • R. P. Isaacs. "Monodiffric Functions." In Construction and Applications of Conformal Maps, Proceedings of a Symposium, pp. 257–266, National Bureau of Standards Appl. Math. Ser. 18. Washington, D.C.: U.S. Government Printing Office, 1952.
  • R. Kenyon. "Conformal Invariance of Domino Tiling." Ann. Probab. 28 (2000), 759–795.
  • C. O. Kiselman. "Functions on Discrete Sets Holomorphic in the Sense of Isaacs, or Monodiffric Functions of the First Kind." Sci. China Ser. A 48 (2005), 86–96.
  • A. Nakamura and A. Rosenfeld. "Digital Calculus." Inform. Sci. 98:1–4 (1997), 83–98.
  • S. P. Novikov. "Schrödinger Operators on Graphs and Symplectic Geometry." In The Arnoldfest, edited by E. Bierstone, B. Khesin, A. Khovanskii, and J. Marsden, pp. 397–413, Fields Institute Communications 24. Providence, RI: American Math. Soc., 1999.
  • I. Porteous. Clifford Algebras and the Classical Groups, Cambridge Studies in Advanced Mathematics 50. Cambridge: Cambridge University Press, 1995.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.