Advertisement

Journal of Mathematical Sciences

, Volume 151, Issue 5, pp 3372–3430 | Cite as

Two-sided Laplace transform over Cayley-Dickson algebras and its applications

  • S. V. Ludkovsky
Article

Keywords

Closed Interval Discontinuity Point Integral Converge Fubini Theorem Euler Integral 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. C. Baez, “The octonions,” Bull. Amer. Math. Soc., 39, No. 2, 145–205 (2002).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    F. A. Berezin, Introduction to Superanalysis, D. Reidel, Kluwer Group, Dordrecht (1987).MATHGoogle Scholar
  3. 3.
    G. Emch, “Mèchanique quantique quaternionienne et relativitè restreinte,” Helv. Phys. Acta, 36, 739–788 (1963).MathSciNetGoogle Scholar
  4. 4.
    F. Gürsey and C.-H. Tze, On the Role of Division, Jordan and Related Algebras in Particle Physics, World Scientific, Singapore (1996).MATHGoogle Scholar
  5. 5.
    W. R. Hamilton, Selected Works. Optics. Dynamics. Quaternions [Russian translation], Nauka, Moscow (1994).Google Scholar
  6. 6.
    I. L. Kantor and A. S. Solodovnikov, Hypercomplex Numbers, Springer-Verlag, Berlin (1989).MATHGoogle Scholar
  7. 7.
    A. Khrennikov, “Superanalysis,” Series Mathematics and Its Applications, 470, Kluwer Acad. Publ., Dordrecht (1999).Google Scholar
  8. 8.
    A. G. Kurosh, Lectures on General Algebra [in Russian], Nauka, Moscow (1973).Google Scholar
  9. 9.
    M. A. Lavrentiev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1987).Google Scholar
  10. 10.
    H. B. Lawson, and M.-L. Michelson, Spin Geometry, Princeton Univ. Press, Princeton (1989).MATHGoogle Scholar
  11. 11.
    S. V. Ludkovsky, “Functions of several variables of Cayley-Dickson numbers and manifolds over them,” in: Contemporary Mathematics and Its Applications [in Russian] 28, Institute of Cybernetics, Tbilisi (2005).Google Scholar
  12. 12.
    S. V. Ludkovsky, “Differential functions of Cayley-Dickson numbers and integration along paths,” in: Contemporary Mathematics and Its Applications [in Russian], 28, Institute of Cybernetics, Tbilisi (2005).Google Scholar
  13. 13.
    S. V. Ludkovsky and F. van Oystaeyen, “Differentiable functions of quaternion variables,” Bull. Sci. Math., 127, 755–796 (2003).CrossRefMathSciNetGoogle Scholar
  14. 14.
    F. van Oystaeyen, “Algebraic geometry for associative algebras,” Lect. Notes Pure Appl. Math., 232 (2000).Google Scholar
  15. 15.
    B. van der Pol and H. Bremmer, Operational Mathcalculus Based on the Two-Sided Laplace Integral, Cambridge Univ. Press, Cambridge (1964).Google Scholar
  16. 16.
    A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series [in Russian], Nauka, Moscow (1981).MATHGoogle Scholar
  17. 17.
    H. Rothe, “Systeme Geometrischer Analyse,” in: Encyklopädie der Mathematischen Wissenschaften. Band 3. Geometrie, 1277–1423, Teubner, Leipzig (1914–1931).Google Scholar
  18. 18.
    W. Rudin, Foundations of Mathematical Analysis [Russian translation], Mir, Moscow (1976).Google Scholar
  19. 19.
    M. A. Soloviev, “Structure of the space of non-Abelian gauge fields,” In: Proceedings of the P. N. Lebedev Physical Institute [in Russian], 210, 112–155 (1993).Google Scholar
  20. 20.
    E. H. Spanier, Algebraic Topology, Academic Press, New York (1966).MATHGoogle Scholar
  21. 21.
    V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1971).Google Scholar
  22. 22.
    V. A. Zorich, Mathematical Analysis [in Russian], Vol. 2, Nauka, Moscow (1984).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Department of Applied MathematicsMoscow State Technical University MIREAMoscowRussia

Personalised recommendations