On the Structure of the Taylor Series in Clifford and Quaternionic Analysis

Integral Equations and Operator Theory

Volumn 71, Issue 3, 2011, Pages 311-326

  Alpay, Daniel ^a   de María Correa Romero, Flor ^b   Luna Elizarrarás, María Elena ^b   Shapiro, Michael ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

Author keywords

Clifford and quaternionic analysis; Fueter variables; hyperholomorphic functions; Taylor series

Indexed keywords

EID: 80255141855     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00020-011-1909-9     Document Type: Article

References (13)

1. Alpay D., Correa-Romero F. M., Luna-Elizarrarás M. E., Shapiro M.: Hyperholomorphic rational functions: the Clifford analysis case. Complex Var. Elliptic Equ. 52(1), 59-78 (2007).
2. Alpay D., Correa-Romero F. M., Luna-Elizarrarás M. E., Shapiro M.: Fonctions rationnelles et problème de Gleason associés à l'opérateur de Dirac. Comtes-Rendus Mathématiques (Paris) Ser. I 343(5), 291-295 (2006).
3. Alpay D., Schneider B., Shapiro M., Volok D.: Fonctions rationnelles et théorie de la réalisation: le cas hyper-analytique. Comptes-Rendus de l'Acadèmie des Sciences (Paris) 336, 975-980 (2003).
4. Alpay D., Shapiro M.: Problème de Gleason et interpolation pour les fonctions hyper-analytiques. Comptes-Rendus de l'Acadèmie des Sciences, Mathematique, Ser. I (Paris) 335, 889-894 (2002).
5. Alpay D., Shapiro M.: Gleason's problem and tangential homogeneous interpolation for hyperholomorphic quaternionic functions. Complex Var. 48, 877-894 (2003).
6. 4. J. Funct. Anal. 221(1), 122-149 (2005).
7. Bock S., Gürlebeck K.: On a generalized Appell system and monogenic power series. Math. Meth. Appl. Sci. 33(4), 394-411 (2010).
8. Bock, S., Gürlebeck, K., Lavicka, R., Soucek, V.: The Gelfand-Tsetlin bases for spherical monogenics in dimension 3 (2010). arXiv: 1010. 1615v2 [math. CV].
9. Brackx, F., Delanghe, R., Sommen, F. Clifford analysis. In: Research Notes in Mathematics, vol. 76. Pitman, London (1982).
10. Delanghe, R., Sommen, F., Souček, V.: Clifford algebra and spinor-valued functions. In: Mathematics and its Applications, p. 53. Kluwer Academic Publishers, Dordrecht (1992).
11. Fueter, R.: Die Theorie der regülaren Funktionen einer quaternionen Variablen. Comptes rendus du congrès international des mathématiciens, Oslo 1936, Tome I, pp. 75-91 (1937).
12. Gürlebeck K., Sprössig W.: Quaternionic and Clifford Calculus for Physicists and Engineers. Wiley, New York (1997).
13. m+1 based on a permutational product. Complex Var. Theory Appl. 15, 181-191 (1990).