Hypercomplex algebras, hypercomplex analysis and conformal invariance

John Ryan

Compositio Mathematica (1987)

  • Volume: 61, Issue: 1, page 61-80
  • ISSN: 0010-437X

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Ryan, John. "Hypercomplex algebras, hypercomplex analysis and conformal invariance." Compositio Mathematica 61.1 (1987): 61-80. <http://eudml.org/doc/89815>.

@article{Ryan1987,
author = {Ryan, John},
journal = {Compositio Mathematica},
keywords = {hypercomplex analysis; Function theories over Clifford algebras; hypercomplex algebra; generalized Cauchy-Riemann equations},
language = {eng},
number = {1},
pages = {61-80},
publisher = {Martinus Nijhoff Publishers},
title = {Hypercomplex algebras, hypercomplex analysis and conformal invariance},
url = {http://eudml.org/doc/89815},
volume = {61},
year = {1987},
}

TY - JOUR
AU - Ryan, John
TI - Hypercomplex algebras, hypercomplex analysis and conformal invariance
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 61
IS - 1
SP - 61
EP - 80
LA - eng
KW - hypercomplex analysis; Function theories over Clifford algebras; hypercomplex algebra; generalized Cauchy-Riemann equations
UR - http://eudml.org/doc/89815
ER -

References

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  3. [3] F. Brackx, R. Delanghe and F. Sommen: Clifford analysis. Research Notes in Mathematics, No. 76Pitman (1982). Zbl0529.30001
  4. [4] J. Bures and V. Soucek: Generalized hypercomplex analysis and its integral formulae. To appear in Complex Variables: Theory and Application. Zbl0586.30043
  5. [5] R. Delanghe: On regular-analytic functions with values in a Clifford algebra. Mathematische Annalen185 (1970) 91-111. Zbl0176.37904MR265618
  6. [6] R. Delanghe and F. Brackx: Hypercomplex function theory and Hilbert modules with reproducing kernel. Proceedings of the London Mathematical Society37 (1978) 545-576. Zbl0392.46019MR512025
  7. [7] R. Feuter: Über die Analytische Darstellung der Relulären Funktionen einer Quaternionenvariablen. Commentarii Mathematici Helvetici8 (1936) 371-381. JFM62.0120.04
  8. [8] R. Feuter: Functions of a Hypercomplex Variable. Lecture Notes, University of Zurich (1948) written and supplemented by E. Bareiss. 
  9. [9] C.D. Gay and D.E. Littlewood: Analyatic spinor fields. Proceedings of the Royal SocietyA313 (1969) 491-507. Zbl0182.43301MR251657
  10. [10] L. Gross: Norm invariance of mass-zero equations under the conformal group. J. of Mathematical Physics5 (1964) 687-698. Zbl0127.39306MR164632
  11. [11] F. Gursey and H.C. Tse: Complex and quaternionic analyticity in chiral and gauge theories. Annals of Physics128 (1980) 29-130. Zbl0457.30039MR587683
  12. [12] K. Imaeda: A new formulation of classical electrodynamics. Nuovo Cimento32B (1976) 138-162. MR408457
  13. [13] H.P. Jakobsen and M. Vergne: Wave and Dirac operators, and representations of the conformal group. J. of Functional Analysis24 (1977) 52-106. Zbl0361.22012MR439995
  14. [14] M.A.M. Murray: The Cauchy integral, Caldéron commutators and conjugations of singular integral in Rn. Trans. Am. Math. Soc.289 (1985) 497-518. Zbl0574.42012MR784001
  15. [15] I. Porteous: Topological Geometry. Van Nostrand Company (1969). Zbl0186.06304MR254852
  16. [16] J. Ryan: Complexified Clifford analysis. Complex Variables: Theory and Application1 (1982) 119-149. Zbl0503.30039MR674364
  17. [17] J. Ryan: Extensions of Clifford analysis to complex, finite dimensional, associative algebras with identity. Proceedings of the Royal Irish Academy84A (1984) 37-50. Zbl0557.30043MR771644
  18. [18] J. Ryan: Conformal Clifford manifolds arising in Clifford analysis. Proceedings of the Royal Irish Academy85A (1985) 1-23. Zbl0581.32007MR821418
  19. [19] F. Sommen: Spherical monogenics and analytic functionals on the unit sphere. Tokyo Journal of Mathematics4 (1981) 427-456. Zbl0481.30040MR646051
  20. [20] F. Sommen: Some connections between Clifford analysis and complex analysis. Complex Variables: Theory and Application1 (1982) 98-118. Zbl0464.30039MR674363
  21. [21] F. Sommen: Special functions in Clifford analysis and axial symmetry, to appear. Zbl0634.30042
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