SpringerLink
Log in

The Octonionic Bergman Kernel for the Unit Ball

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

By introducing a suitable new definition for the inner product of the octonionic Bergman space on the unit ball, we determine the explicit form of the octonionic Bergman kernel for the unit ball, in the framework of octonionic analysis which is non-commutative and non-associative.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baez, J.C.: The octonions. Bull. Am. Math. Soc. 39(2), 145–205 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis. Research Notes in Mathematics, vol. 76. Pitman Advanced Publishing Program, Boston (1982)

    MATH  Google Scholar 

  3. Dentoni, P., Sce, M.: Funzioni regolari nell’algebra di Cayley. Rend. Sem. Mat. Univ. Padova. 50, 251–267 (1973)

    MathSciNet  MATH  Google Scholar 

  4. Hurwitz, A.: Über die Composition der quadratischen Formen von beliebig vielen Variablen. Nachr. Ges. Wiss. Gött. 1898, 309–316 (1898)

    MATH  Google Scholar 

  5. Jacobson, N.: Basic Algebra I, 2nd edn. W. H. Freeman and Company, New York (1985)

    MATH  Google Scholar 

  6. Li, X.: Octonionic analysis. Ph.D. Thesis, Peking University (1998)

  7. Li, X., Peng, L.: On Stein-Weiss conjugate harmonic function and octonion analytic function. Approx. Theory & its Appl. 16(2), 28–36 (2000)

    MathSciNet  MATH  Google Scholar 

  8. Li, X., Peng, L.: The Cauchy integral formulas on the octonions. Bull. Belg. Math. Soc. 9(1), 47–64 (2002)

    MathSciNet  MATH  Google Scholar 

  9. Li, X., Wang, J.: Orthogonal invariance of the Dirac operator and the critical index of subharmonicity for octonionic analytic functions. Adv. Appl. Clifford Algebras 24(1), 141–149 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, X., Zhao, K., Peng, L.: The Laurent series on the octonions. Adv. Appl. Clifford Algebras 11(S2), 205–217 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, X., Zhao, K., Peng, L.: Characterization of octonionic analytic functions. Complex Variables 50(13), 1031–1040 (2005)

    MathSciNet  MATH  Google Scholar 

  12. Li, X., Peng, L., Qian, T.: Cauchy integrals on Lipschitz surfaces in octonionic spaces. J. Math. Anal. Appl. 343(2), 763–777 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, X., Peng, L., Qian, T.: The Paley-Wiener theorem in the non-commutative and non-associative octonions. Sci. China Ser. A 52(1), 129–141 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liao, J., Li, X., Wang, J.: Orthonormal basis of the octonionic analytic functions. J. Math. Anal. Appl. 366(1), 335–344 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, J., Li, X., Liao, J.: The quaternionic Cauchy–Szegö kernel on the quaternionic Siegel half space. ar**v:1210.5086v1

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Guangdong University of Foreign Studies, Guangzhou, 510006, China

    **xun Wang

  2. School of Computer Sciences, South China Normal University, Guangzhou, 510631, China

    **ngmin Li

Authors
  1. **xun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **ngmin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to **xun Wang.

Additional information

Communicated by Hendrik De Bie

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, J., Li, X. The Octonionic Bergman Kernel for the Unit Ball. Adv. Appl. Clifford Algebras 28, 60 (2018). https://doi.org/10.1007/s00006-018-0877-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00006-018-0877-4

Keywords

Mathematics Subject Classification

Search

Navigation