Acta mathematica scientia, Series B >
A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS
Received date: 2006-04-25
Revised date: 2007-07-02
Online published: 2011-01-20
Supported by
The research was partly supported by NSFs of China (10771059 and 11071063) and Hunan Province (05JJ10001), and NCET (04-0783).
In this article, a sufficient condition for a Clifford continued fraction to be convergent is established, and some applications are given.
LI Yong-Qun , WANG Xian-Tao . A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 8 -14 . DOI: 10.1016/S0252-9602(11)60202-6
[1] Ahlfors L V, Lounesto P. Some remarks on Clifford algebra. Complex Variables, 1989, 12: 201--209
[2] Ahlfors L V. Möbius transformations and Clifford numbers//Differential Geometry and Complex Analysis, H. E. Rauch Memorial Volume. New York: Springer-Verlag, 1985
[3] Ahlfors L V. On the fixed points of Möbius transformations in Rn. Ann Acad Sci Fen Ser A I Math, 1985, 10: 15--27
[4] Beardon A F. Continued fractions, discrete groups and complex dynamics. Comput Methods and Function Theory, 2001, 1: 535--594
[5] Beardon A F. Continued fractions, Möbius transformations and Cliffod algebras. Bull London Math Soc, 2003, 35: 302--308
[6] Beardon A F. Hillam-Thron theorem in higher dimensions. Geom Dedicata, 2003, 96: 205--209
[7] Jones W B, Thron W J. Continued Fractions: Analytic Theory and Applications, Encyclopedia of Mathematics and its Applications. Mass: Addison-Wesley Publishing Co, 1980
[8] Mustapha Raissouli, Ali Kacha. Convergence of matrix continued fractions. Linear Algebra Appl, 2000, 320: 115--129
[9] Li Y, Chen J. Value regions and element regions of Clifford continued fractions. J Natural Science of Heilongjiang University, 2008, 25: 178--182
[10] Li Y. Three term recurrence relation and Pincherle theroem for Clifford continued fractions. Adv in Math (China), 2008, 37: 15--24
[11] Lorentzen L, Waadeland H. Continued Fractions with Applications, Studies in Computational Mathematics 3. Amsterdam: North-Holland Publishing Co, 1992
[12] Wang X, Yang W. Discreteness criteria of M\"obius groups of high dimensions and convergence theorem of Kleinian groups. Adv in Math, 2001, 159: 68--82
[13] Zhao H, Zhu G. A Worpitzky theorem for vector valued continued fractions. J Comput Appl Math, 2003, 154: 107--114
[14] Zhao H, Zhu G. Matrix-valued continued fractions. J Approx Theory, 2003, 120: 136--152
/
| 〈 |
|
〉 |