126
Views
1
CrossRef citations to date
0
Altmetric
Articles

Split-quaternionic Hermitian Clifford analysis

, &
Pages 333-353 | Received 10 May 2013, Accepted 03 Jun 2014, Published online: 26 Aug 2014

References

  • Frenkel I, Libine M. Split quaternionic analysis and separation of the series for SL(2, ℝ) and SL(2, ℂ)/SL(2, ℝ). Adv. Math. 2011;228:678–763.
  • Cortes V. Handbook of pseudo-Riemannian geometry and supersymmetry. Vol. 16, IRMA lectures in mathematics and theoretical physics. Zürich: European Mathematical Society; 2010.
  • Brody DC, Graefe E. On complexified mechanics and coquaternions. J. Phys. A. 2011;44:072001 9pp.
  • Brackx F, Delanghe R, Sommen F. Clifford analysis. Boston: Pitman; 1982.
  • Delanghe R, Sommen F, Souček V. Clifford algebra and spinor-valued functions. Dordrecht: Kluwer; 1992.
  • Gilbert J, Murray M. Clifford algebras and Dirac operators in harmonic analysis. Cambridge: Cambridge University Press; 1991.
  • Gürlebeck K, Habetha K, Sprössig W. Holomorphic functions in the plane and n-dimensional space. Basel: Birkhäuser; 2008.
  • Gürlebeck K, Sprössig W. Quaternionic analysis and elliptic boundary value problems. Vol. 89, International series of numerical mathematics. Basel: Birkhäuser; 1990.
  • Brackx F, Bureš J, De Schepper H, Ewlbode D, Sommen F, Souček V. Fundaments of Hermitean Clifford analysis part I: complex structure. Complex Anal. Oper. Theory. 2007;1:341–365.
  • Brackx F, Bureš J, De Schepper H, Ewlbode D, Sommen F, Souček V. Fundaments of Hermitean Clifford analysis part II: splitting of h-monogenic equations. Complex Var. Elliptic Equ. 2007;52:1063–1079.
  • Sabadini I, Sommen F. Hermitian Clifford analysis and resolutions. Math. Meth. Appl. Sci. 2002;25:1395–1413.
  • Peña-Peña D, Sabadini I, Sommen F. Quaternionic Clifford analysis: the Hermitian setting. Complex Anal. Oper. Theory. 2007;1:97–113.
  • Damiano A, Eelbode D, Sabadini I. Quaternionic Hermitian spinor systems and compatibility conditions. Adv. Geom. 2011;11:169–189.
  • Rocha-Chávez R, Shapiro M, Sommen F. Integral theorems for functions and differential forms in ℂm. Vol. 428, Research Notes in Mathematics. New York (NY): Chapman &Hall/CRC; 2002.
  • Price GB. An introduction to multicomplex spaces and functions. New York (NY): Marcel Dekker; 1991.
  • Catoni F, Cannata R, Zampetti P. An introduction to commutative quaternions. Adv. Appl. Clifford Algebr. 2006;16:1–28.
  • Abreu-Blaya R, Bory-Reyes J, Brackx F, De Schepper H, Sommen F. Cauchy integral formulae in quaternionic Hermitean Clifford analysis. Complex Anal. Oper. Theory. 2012;6:971–985.
  • Kytmanov A. The Bochner–Martinelli Integral and its applications. Basel: Birkhäuser; 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.