Hypercomplex algebras, hypercomplex analysis and conformal invariance
Ryan, John
Compositio Mathematica, Tome 61 (1987), p. 61-80 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1987-01-01
@article{CM_1987__61_1_61_0,
     author = {Ryan, John},
     title = {Hypercomplex algebras, hypercomplex analysis and conformal invariance},
     journal = {Compositio Mathematica},
     volume = {61},
     year = {1987},
     pages = {61-80},
     mrnumber = {879189},
     zbl = {0609.32005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1987__61_1_61_0}
}

Ryan, John. Hypercomplex algebras, hypercomplex analysis and conformal invariance. Compositio Mathematica, Tome 61 (1987) pp. 61-80. http://gdmltest.u-ga.fr/item/CM_1987__61_1_61_0/

[1] L.V. Ahlfors: Complex analysis. Second edition McGraw Hill (1966). | MR 188405 | Zbl 0154.31904

[2] M.F. Atiyah, R. Bott and A. Shapiro: Clifford modules. Topology 3 (1965) 3-38. | MR 167985 | Zbl 0146.19001

[3] F. Brackx, R. Delanghe and F. Sommen: Clifford analysis. Research Notes in Mathematics, No. 76 Pitman (1982). | Zbl 0529.30001

[4] J. Bures and V. Soucek: Generalized hypercomplex analysis and its integral formulae. To appear in Complex Variables: Theory and Application. | Zbl 0586.30043

[5] R. Delanghe: On regular-analytic functions with values in a Clifford algebra. Mathematische Annalen 185 (1970) 91-111. | MR 265618 | Zbl 0176.37904

[6] R. Delanghe and F. Brackx: Hypercomplex function theory and Hilbert modules with reproducing kernel. Proceedings of the London Mathematical Society 37 (1978) 545-576. | MR 512025 | Zbl 0392.46019

[7] R. Feuter: Über die Analytische Darstellung der Relulären Funktionen einer Quaternionenvariablen. Commentarii Mathematici Helvetici 8 (1936) 371-381. | JFM 62.0120.04

[8] R. Feuter: Functions of a Hypercomplex Variable. Lecture Notes, University of Zurich (1948) written and supplemented by E. Bareiss.

[9] C.D. Gay and D.E. Littlewood: Analyatic spinor fields. Proceedings of the Royal Society A313 (1969) 491-507. | MR 251657 | Zbl 0182.43301

[10] L. Gross: Norm invariance of mass-zero equations under the conformal group. J. of Mathematical Physics 5 (1964) 687-698. | MR 164632 | Zbl 0127.39306

[11] F. Gursey and H.C. Tse: Complex and quaternionic analyticity in chiral and gauge theories. Annals of Physics 128 (1980) 29-130. | MR 587683 | Zbl 0457.30039

[12] K. Imaeda: A new formulation of classical electrodynamics. Nuovo Cimento 32B (1976) 138-162. | MR 408457

[13] H.P. Jakobsen and M. Vergne: Wave and Dirac operators, and representations of the conformal group. J. of Functional Analysis 24 (1977) 52-106. | MR 439995 | Zbl 0361.22012

[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. | MR 784001 | Zbl 0574.42012

[15] I. Porteous: Topological Geometry. Van Nostrand Company (1969). | MR 254852 | Zbl 0186.06304

[16] J. Ryan: Complexified Clifford analysis. Complex Variables: Theory and Application 1 (1982) 119-149. | MR 674364 | Zbl 0503.30039

[17] J. Ryan: Extensions of Clifford analysis to complex, finite dimensional, associative algebras with identity. Proceedings of the Royal Irish Academy 84A (1984) 37-50. | MR 771644 | Zbl 0557.30043

[18] J. Ryan: Conformal Clifford manifolds arising in Clifford analysis. Proceedings of the Royal Irish Academy 85A (1985) 1-23. | MR 821418 | Zbl 0581.32007

[19] F. Sommen: Spherical monogenics and analytic functionals on the unit sphere. Tokyo Journal of Mathematics 4 (1981) 427-456. | MR 646051 | Zbl 0481.30040

[20] F. Sommen: Some connections between Clifford analysis and complex analysis. Complex Variables: Theory and Application 1 (1982) 98-118. | MR 674363 | Zbl 0464.30039

[21] F. Sommen: Special functions in Clifford analysis and axial symmetry, to appear. | Zbl 0634.30042

[22] V. Soucek: Complex quaternionic analysis applied to spin 1/2 massless fields. Complex Variables: Theory and Application 1 (1983) 327-346. | MR 706989 | Zbl 0525.30039

[23] A. Sudbery: Quaternionic analysis. Mathematical Proceedings of the Cambridge Philosophical Society 85 (1979) 199-225. | MR 516081 | Zbl 0399.30038

[24] N.J. Vilenkin: Special Functions and the Theory of Group Representations Translations of Mathematical Monographs. American Mathematical Society 22 (1968). | MR 229863 | Zbl 0172.18404