Hurwitz analysis: basic concepts and connection with Clifford analysis

Enrique Ramírez de Arellano; Nikolai Vasilevski; Michael Shapiro

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 209-221
  • ISSN: 0137-6934

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Ramírez de Arellano, Enrique, Vasilevski, Nikolai, and Shapiro, Michael. "Hurwitz analysis: basic concepts and connection with Clifford analysis." Banach Center Publications 37.1 (1996): 209-221. <http://eudml.org/doc/208599>.

@article{RamírezdeArellano1996,
author = {Ramírez de Arellano, Enrique, Vasilevski, Nikolai, Shapiro, Michael},
journal = {Banach Center Publications},
keywords = {Clifford algebra; multiplication in the Hurwitz pair; generalized Cauchy-Riemann operators; kernels; Hurwitz analysis; Clifford analysis},
language = {eng},
number = {1},
pages = {209-221},
title = {Hurwitz analysis: basic concepts and connection with Clifford analysis},
url = {http://eudml.org/doc/208599},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Ramírez de Arellano, Enrique
AU - Vasilevski, Nikolai
AU - Shapiro, Michael
TI - Hurwitz analysis: basic concepts and connection with Clifford analysis
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 209
EP - 221
LA - eng
KW - Clifford algebra; multiplication in the Hurwitz pair; generalized Cauchy-Riemann operators; kernels; Hurwitz analysis; Clifford analysis
UR - http://eudml.org/doc/208599
ER -

References

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  1. [BDS] F. Brackx, R. Delanghe, F. Sommen, Clifford Analysis, Pitman Research Notes in Math. 76, 1982. 
  2. [H1] A. Hurwitz, Über die Komposition der quadratischen Formen von beliebig vielen Variablen, Nachrichten von der Königlichen Gesellschaft der Wiessenschaften zu Göttingen Math. phys. Kl. (1898), 308-316, reprinted in: A. Hurwitz, Mathematische Werke II, Birkhäuser Verlag, Basel, 1933, 565-571. 
  3. [H2] A. Hurwitz, Über die Komposition der quadratischen Formen, Math. Ann. 88 (1923), 1-25, reprinted in: A. Hurwitz, Mathematische Werke II, Birkhäuser Verlag, Basel, 1933, 641-666. 
  4. [KR1] W. Królikowski and E. Ramírez de Arellano, Fueter-Hurwitz regular mappings and an integral representation, in: Clifford Algebras and Their Applications in Mathematical Physics, A. Micali et al., eds., Kluwer Acad. Publishers, Dordrecht 1992, 221-237. Zbl0769.30040
  5. [KR2] W. Królikowski and E. Ramírez de Arellano, Polynomial solutions of the Fueter-Hurwitz equation, Cont. Math. 137 (1992), 297-305. Zbl0767.30038
  6. [LR] J. Ławrynowicz and J. Rembieliński, Pseudo-euclidean Hurwitz pairs and generalized Fueter equations, in: Clifford Algebras and Their Applications in Mathematical Physics, J.S.R. Chisholm and A.K. Common, eds., D. Reidel Publ. Co., Dordrecht 1986, 39-48. 
  7. [RSV1] E. Ramírez de Arellano, M. V. Shapiro, N. L. Vasilevski, A canonical relation between Hurwitz pairs and Clifford algebras, Reporte Interno No. 112, Dep. Mat., CINVESTAV del IPN., Mexico City, 1993, 34 pp. 
  8. [RSV2] E. Ramírez de Arellano, Hurwitz pairs and Clifford algebra representations, in: Clifford Algebras and Their Applications in Mathematical Physics, F. Brackx, R. Delanghe and H. Serras eds., Kluwer Acad. Publishers, Dordrecht 1993, 171-181. 
  9. [S] M. V. Shapiro, Some remarks on generalizations of the one-dimensional complex analysis: hypercomplex approach, Reporte Interno No. 131, Dep. Mat., CINVESTAV del IPN., Mexico City, 1993, 23 pp. 
  10. [Sh] D. B. Shapiro, Products of sums of squares, Expo. Math. 2 (1984), 235-261. Zbl0541.10025
  11. [SY] T. L. Smith and P. Yiu, Construction of sums of squares formulae with integer coefficients, Bol. Soc. Mat. Mexicana (2) 37 (1992), 479-495. Zbl0830.11018

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