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关于Clifford连分式的三项递推关系和Pincherle’s定理(英文) 被引量：1

Three-term Recurrence Relations and Pincherle's Theorem for Clifford Valued Continued Fractions
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摘要 本文建立了Clifford连分式的三项递推关系和Pincherle's定理,并给出了它们的应用,也获得了关于Clifford连分式的矩阵递推关系的最小解的几个性质. In this paper, three-term recurrence relations and Pincherle＇s theorem are established for Clifford valued continued fractions, and their applications are given. Also several properties of the minimal solution of matrix recurrence relations about Clifford valued continued fractions are obtained.
作者 李永群
机构地区 湖南大学数学与计量经济学院
出处 《数学进展》 CSCD 北大核心 2008年第1期15-24,共10页 Advances in Mathematics（China）
基金 The research was partly supported by NSFC(No．10571048)；；Hunan Province(No．05JJ10001)；；NCET(No．04-0783)．
关键词 Clifford连分式 三项递推关系 Pincherle’s定理 应用 最小解 Clifford valued continued fraction three-term recurrence relations Pincherle＇s theorem application minimal solution
分类号 O174.51 [理学—基础数学]
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参考文献13

  • 1Ahlbrandt, C.D., A Pincherle theorem for matrix continued fractions, J. Approximation Theory, 1996, 84: 188-196.
  • 2Ahlfors, L.V. and Lounesto, P., Some remarks on Clifford algebra, Complex Variables, 1989, .12: 201-209.
  • 3Ahlfors, L.V., Mobius Transformations and Clifford Numbers, Differential Geometry and Complex Analysis, H. E. Rauch Memorial Volume, Springer-Verlag, New York, 1985.
  • 4Ahlfors, L.V., On the fixed points of Mobius transformations in R^n, Ann. Acad. Sci. Fen. Ser. A. I. Math., 1985, 10: 15-27.
  • 5Beardon, A.F., Continued fractions, discrete groups and complex dynamics, Computational Methods and Function Theory, 2001, 1: 535-594.
  • 6Beardon, A.F., Continued fractions, Mobius transformations and Cliffod algebras, Bull. London Math. Soc. 2003, 35: 302-308.
  • 7Beardon, A.F., Hillam-Thron theorem in higher dimensions, Geom. Dedicata, 2003, 96: 205-209.
  • 8Jones, W.B. and Thron, W.J., Continued Fractions: Analytic Theory and Applications, Encyclopedia of Mathematics and its Applications, Addison-Wesley, 1980.
  • 9Mustapha Raissouli and Ali Kacha, Convergence of matrix continued fractions, Linear Algebra and Applications, 2000, 320: 115-129.
  • 10Li Y., Chen J., Value regions and element regions of Clifford valued continued fractions, submitted.

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数学进展
2008年 第1期

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