Regular and biregular functions in the sense of Fueter - some problems

W. Królikowski; R. Michael Porter

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 1, page 53-64
  • ISSN: 0066-2216

Abstract

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The biregular functions in the sense of Fueter are investigated. In particular, the class of LR-biregular mappings (left regular with a right regular inverse) is introduced. Moreover, the existence of non-affine biregular mappings is established via examples. Some applications to the quaternionic manifolds are given.

How to cite

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W. Królikowski, and R. Michael Porter. "Regular and biregular functions in the sense of Fueter - some problems." Annales Polonici Mathematici 59.1 (1994): 53-64. <http://eudml.org/doc/262347>.

@article{W1994,
abstract = {The biregular functions in the sense of Fueter are investigated. In particular, the class of LR-biregular mappings (left regular with a right regular inverse) is introduced. Moreover, the existence of non-affine biregular mappings is established via examples. Some applications to the quaternionic manifolds are given.},
author = {W. Królikowski, R. Michael Porter},
journal = {Annales Polonici Mathematici},
keywords = {quaternionic analysis; quaternionic manifolds; biregular functions; non-affine biregular mappings},
language = {eng},
number = {1},
pages = {53-64},
title = {Regular and biregular functions in the sense of Fueter - some problems},
url = {http://eudml.org/doc/262347},
volume = {59},
year = {1994},
}

TY - JOUR
AU - W. Królikowski
AU - R. Michael Porter
TI - Regular and biregular functions in the sense of Fueter - some problems
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 1
SP - 53
EP - 64
AB - The biregular functions in the sense of Fueter are investigated. In particular, the class of LR-biregular mappings (left regular with a right regular inverse) is introduced. Moreover, the existence of non-affine biregular mappings is established via examples. Some applications to the quaternionic manifolds are given.
LA - eng
KW - quaternionic analysis; quaternionic manifolds; biregular functions; non-affine biregular mappings
UR - http://eudml.org/doc/262347
ER -

References

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  1. [1] E. Bonan, Sur les G-structures de type quaternionien, Cahiers Topologie Géom. Différentielle 9 (1967), 389-461. Zbl0171.20802
  2. [2] M. L. Curtis, Matrix Groups, Springer, 1984. 
  3. [3] R. Fueter, Die Funktionentheorie der Differentialgleichungen Δu = 0 und ΔΔu = 0 mit vier reellen Variablen, Comment. Math. Helv. 7 (1935), 307-330. Zbl61.1131.05
  4. [4] R. Fueter, Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen, ibid. 8 (1936), 371-378. Zbl62.0120.04
  5. [5] W. Królikowski, Quaternionic mappings and harmonicity, preprint. Zbl1087.58502
  6. [6] W. Królikowski and E. Ramírez de Arellano, Fueter-Hurwitz regular mappings and an integral representation, in: Clifford Algebras and their Applications in Mathematical Physics, Proceedings, Montpellier, 1989, A. Micali et al. (eds.), Kluwer Acad. Publ., Dordrecht, 1990, 221-237. Zbl0769.30040
  7. [7] W. Królikowski and E. Ramírez de Arellano, On polynomial solutions of the Fueter-Hurwitz equation, in: Proc. Internat. Conf. on Complex Analysis, June 1991, University of Wisconsin, Madison, A. Nagel and E. Lee Stout (eds.), Contemp. Math. 137, Amer. Math. Soc., 1992, 297-305. Zbl0767.30038
  8. [8] R. Narasimhan, Analysis on Real and Complex Manifolds, North-Holland, Amsterdam, 1968. Zbl0188.25803
  9. [9] M. V. Shapiro and N. Vasilevski, Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems, I, II, Complex Variables Theory Appl., to appear. Zbl0847.30033
  10. [10] A. J. Sommese, Quaternionic manifolds, Math. Ann. 212 (1975), 191-214. Zbl0299.53023
  11. [11] V. Souček, Holomorphicity in quaternionic analysis, Seminari di Geometria 1982-1983, Università di Bologna, Istituto de Geometria, Dipartimento de Matematica, 1984. 
  12. [12] A. Sudbery, Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. 85 (1979), 199-225. Zbl0399.30038

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