ALTERNATIVE TO THE HYPERCOMPLEX
FOURIER TRANSFORM DEFINITION
C.A.P. Martinez1, A.L.M. Martinez1
1,2DAMAT
Federal Technological University of Paraná
CEP: 86300-000, Cornélio Procópio, PR, BRASIL

Abstract

In this paper we present a construction of the quaternionic hypercomplex version of Fourier Series and an introduction of a simple quaternionic expansion of Fourier Transform in hypercomplex exponentials is provided. By some examples, we show how the representation is written by using the proposed expansion.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 29
Issue: 6
Year: 2016

DOI: 10.12732/ijam.v29i6.5

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] L. Sinegre, Quaternions and the motion of a solid body about a fixed point according to Hamilton, Rev.-Historie-Math., No 1 (1995), 83-109.
  2. [2] T.Y. Lam, Handbook of Algebra, Vol. 3, North-Holland, Amsterdam (2003), 429-454.
  3. [3] S. Eilenberg, I. Niven, The fundamental theorem of algebra for quaternioins, Bull. Amer. Math. Society, 50 (1944), 246-248.
  4. [4] C.A. Pendeza, M.F. Borges, J.M. Machado, C. Oliveira, De Moivre extended equation for octonions and the Power Series, International Journal of Pure and Applied Mathematics, 45, No 2 (2008), 165-170.
  5. [5] J. Marão, M.F. Borges, Liouville’s theorem and power series for quaternionic functions, International Journal of Pure and Appllied Mathematics, 71, No 3 (2011), 383-384.
  6. [6] S. Bock, K. Gurlebeck, On a generalized Appell system and monogenic power series, Math. Methds Appl. Sci., 33, No 4 (2010), 395-411.
  7. [7] W. Rudin, Principles of Mathematical Analysis, 3rd Ed., MacGraw-Hill (1976).
  8. [8] C.A.P. Martinez, M.F. Borges, A.L.M. Martinez and E.V. Castelani, Fourier series for quaternions and the extension of the square of the error theorem, International Journal of Applied Mathematics, 25 (2012), 559-570.
  9. [9] C.A.P. Martinez, M.F. Borges, A.L.M. Martinez and E.V. Castelani, Square of the error octonionic theorem and hypercomplex Fourier series, Tendências em Matemática Aplicada e Computacional, 14 (2013), 483-495.
  10. [10] K. Kodairo, Complex Analysis, Cambridge University Press, Cambridge, 2007.