Skip to main content
SpringerLink
Log in

The Paley-Wiener theorem in the non-commutative and non-associative octonions

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Stein E. Functions of exponential type. Ann of Math, 65: 582–592 (1957)

    Article  MathSciNet  Google Scholar 

  2. Kou K I, Qian T. The Paley-Wiener theorem in R n with the Clifford analysis setting. J Funct Anal, 189: 227–241 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cartan É. Le principe de dualité et la théorie des groupes simple dt semisimples. Bull Sci Math, 49: 361–374 (1925)

    Google Scholar 

  4. Jordan P, von Neumann J, Wiger E. On an algebraic generalization of the quantum mechanical formalism. Ann of Math, 35: 29–64 (1934)

    Article  MathSciNet  Google Scholar 

  5. Baez J C. The octonions. Bull Amer Math Soc, 39: 145–205 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Baez J C. On quaternions and octonions: Their geometry, arithmetic, and symmetry. Bull Amer Math Soc, 42: 229–243 (2005)

    Article  MathSciNet  Google Scholar 

  7. Li X M. On two questions in Clifford analysis and octonion analysis. In: Kajiwara J, Li Z, Shon K H, eds. Finite or Infinite Dimensional Complex Analysis. Lecture Notes in Pure and Applied Math, Vol. 214. New York: Marcel Dekker, 2000, 293–299

    Google Scholar 

  8. Li X M, Peng L Z. Three-line theorems on the octonions. Acta Math Sinica Engl Ser, 3: 483–490 (2004)

    Article  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  10. Li X M, Peng L Z. On Stein-Weiss conjugate harmonic function and octonion analytic function. Approx Theory Appl, 16: 28–36 (2000)

    MATH  MathSciNet  Google Scholar 

  11. Li X M, Peng L Z. Taylor series and orthogonality of the octonion analytic functions. Acta Math Sci Ser B, 21: 323–330 (2001)

    MATH  MathSciNet  Google Scholar 

  12. Li X M. Octonion Analysis. Ph D Thesis. Beijing: Peking University, 1998

    Google Scholar 

  13. Li X M, Kai Z, Peng L Z. Characterization of octonionic analytic functions. Complex Var, 50(13): 1031–1040 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Li X M, Kai Z, Peng L Z. The Laurent series on the octonions. Adv Appl Clifford Analysis, 11(S2): 205–217 (2001)

    Google Scholar 

  15. Peng L Z, Yang L. The curl in 7 dimensional space and its applications. Approx Theory Appl, 15: 66–80 (1999)

    MATH  MathSciNet  Google Scholar 

  16. Li C, McIntosh A, Qian T. Clifford algebras, Fourier transforms, and singular Convolution operators on Lipschitz surfaces. Rev Mat Iberoamericana, 10(3): 665–695 (1994)

    MATH  MathSciNet  Google Scholar 

  17. Brackx F, Delanghe R, Sommen F. Clifford analysis. In: Res Notes in Math, Vol. 76. Boston: Pitman, 1982

    Google Scholar 

  18. Delanghe R, Sommen F, Soucek V. Clifford Algebras and Spinor Valued Functions: A Function Theory for Dirac Operator. Dordrecht: Kluwer Academic, 1992

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer, South China Normal University, Guangzhou, 510631, China

    XingMin Li

  2. LMAM, School of Computer, Peking University, Beijing, 100871, China

    LiZhong Peng

  3. Faculty of Science and Technology, the University of Macau, 3001, Macau, China

    Tao Qian

Authors
  1. XingMin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. LiZhong Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tao Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to XingMin Li.

Additional information

This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, X., Peng, L. & Qian, T. The Paley-Wiener theorem in the non-commutative and non-associative octonions. Sci. China Ser. A-Math. 52, 129–141 (2009). https://doi.org/10.1007/s11425-008-0054-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-008-0054-7

Keywords

MSC(2000)

Search

Navigation