Hyperholomorphic rational functions: the Clifford analysis case

Complex Variables and Elliptic Equations

Volumn 52, Issue 1, 2007, Pages 59-78

  Alpay, D ^a   Correa Romero, F M ^b   Luna Elizarraras M E ^b   Shapiro, M ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

Author keywords

Cauchy Kovalevskaya extension theorem; Gleason's problem; Mathematics Subject Classifications: Primary: 47S10; Rational functions; Realization theory; Secondary: 30G35

Indexed keywords

EID: 49749125239     PISSN: 17476933     EISSN: 17476941     Source Type: Journal    
DOI: 10.1080/17476930600793654     Document Type: Article

References (12)

1. Alpay, D, Schneider, B, Shapiro, M and Volok, D. 2003. Fonctions rationnelles et théorie de la réalisation: le cas hyper-analytique. Comptes Rendus Mathématiques, 336: 975–980.
2. Alpay, D and Shapiro, M. 2002. Problème de Gleason et interpolation pour les fonctions hyper-analytiques. Comptes Rendus Mathematique. Academie des Sciences. Paris, 335: 889–894.
3. Alpay, D, Shapiro, M and Volok, D. 2005. Rational hyperholomorphic functions in. Journal of Functional Analysis, 221: 122–149.
4. Alpay, D, Shapiro, M and Volok, D. 2004. Espaces de de Branges Rovnyak: le cas hyper-analytique. Comptes Rendus Mathématiques, 338: 437–442.
5. Alpay, D, Shapiro, M and Volok, D. 2006. Reproducing kernel spaces of series of Fueter polynomials. Operator Theory: Advances and Applications, 162: 19–45.
6. Bart, H, Gohberg, I and Kaashoek, MA. 1979. “ Volume 1 of Operator Theory: Advances and Applications ”. In Minimal Factorization of Matrix and Operator Functions, Basel: Birkhäuser Verlag.
7. Gürlebeck, K and Sprössig, W. 1997. “ volume 1 of Mathematical methods in practice ”. In Quaternionic and Clifford Calculus for Physicists and Engineers, Chichester: John Wiley and Sons.
8. Laville, G. 1991. On Cauchy–Kovalewski extension. Journal of Functional Analysis, 101 (1): 25–37.
9. Peetre, J. 1992. Reproducing formulae for monogenic functions. Bulletin of Society of Mathematicians. Belgarian Séries B, 44 (2): 171–192.
10. Rudin, W. 1980. Function Theory in the Unit Ball of, Berlin: Springer-Verlag.
11. Rudin, W. 1982. Real and Complex Analysis, New York: McGraw Hill.
12. Sommen, F. 1981. A product and an exponential function in hypercomplex function theory. Applicable Analysis, 12 (1): 13–26.