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The Cauchy-Kovalevskaya extension theorem in discrete Clifford analysis
1. | Cliord Research Group, Faculty of Engineering, Ghent University, Galglaan 2, 9000, Gent, Belgium |
2. | Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, 9000 Gent, Belgium |
3. | Clifford Research Group, Faculty of Sciences, Ghent University, Galglaan 2, 9000 Gent |
References:
[1] |
F. Brackx, R. Delanghe and F. Sommen, "Clifford Analysis," Research Notes in Mathematics, 76, Pitman, London, 1982. |
[2] |
F. Brackx, H. De Schepper, F. Sommen and L. Van de Voorde, Discrete Clifford analysis: an overview, Cubo, 11 (2009), 55-71. |
[3] |
F. Brackx, H. De Schepper, F. Sommen and L. Van de Voorde, Discrete Clifford analysis: a germ of function theory, In: I. Sabadini, M. Shapiro, F. Sommen (eds.), Hypercomplex Analysis, Birkhäuser, (2009), 37-53. |
[4] |
R. Delanghe, F. Sommen and V. Souček, "Clifford Algebra and Spinor-valued Functions - A Function Theory for the Dirac Operator," Kluwer Academic Publishers, Dordrecht, 1992. |
[5] |
A. Cauchy, Oeuvres completes, Série 1, Tome VII, Gauthier-Villars, Paris, 1882-1974, 17-58. |
[6] |
R. Cooke, The Cauchy-Kovalevskaya Theorem (preprint, available online: http://www.cems.uvm.edu/ cooke/ckthm.pdf). |
[7] |
H. De Ridder, H. De Schepper, F. Sommen and U. Kähler, Discrete function theory based on skew Weyl relations, Proc. Amer. Math. Soc., 138 (2010), 3241-3256. |
[8] |
H. De Ridder, H. De Schepper and F. Sommen, Fueter polynomials in discrete Clifford analysis, (submitted). |
[9] |
N. Faustino, U. Kähler and F. Sommen, Discrete Dirac operators in Clifford analysis, Adv. Appl. Cliff. Alg., 17 (2007), 451-467. |
[10] |
J. Gilbert and M. Murray, "Clifford Algebra and Dirac Operators in Harmonic Analysis," Cambridge University Press, Cambridge, 1991. |
[11] |
K. Gürlebeck and W. Sprössig, "Quaternionic and Clifford Calculus for Physicists and Engineers," J. Wiley & Sons, Chichester, 1997. |
[12] |
S. Kowalevsky, Zur Theorie der partiellen Differentialgleichung, J. für die Reine und Angew. Mathem., 80 (1875), 1-32. |
show all references
References:
[1] |
F. Brackx, R. Delanghe and F. Sommen, "Clifford Analysis," Research Notes in Mathematics, 76, Pitman, London, 1982. |
[2] |
F. Brackx, H. De Schepper, F. Sommen and L. Van de Voorde, Discrete Clifford analysis: an overview, Cubo, 11 (2009), 55-71. |
[3] |
F. Brackx, H. De Schepper, F. Sommen and L. Van de Voorde, Discrete Clifford analysis: a germ of function theory, In: I. Sabadini, M. Shapiro, F. Sommen (eds.), Hypercomplex Analysis, Birkhäuser, (2009), 37-53. |
[4] |
R. Delanghe, F. Sommen and V. Souček, "Clifford Algebra and Spinor-valued Functions - A Function Theory for the Dirac Operator," Kluwer Academic Publishers, Dordrecht, 1992. |
[5] |
A. Cauchy, Oeuvres completes, Série 1, Tome VII, Gauthier-Villars, Paris, 1882-1974, 17-58. |
[6] |
R. Cooke, The Cauchy-Kovalevskaya Theorem (preprint, available online: http://www.cems.uvm.edu/ cooke/ckthm.pdf). |
[7] |
H. De Ridder, H. De Schepper, F. Sommen and U. Kähler, Discrete function theory based on skew Weyl relations, Proc. Amer. Math. Soc., 138 (2010), 3241-3256. |
[8] |
H. De Ridder, H. De Schepper and F. Sommen, Fueter polynomials in discrete Clifford analysis, (submitted). |
[9] |
N. Faustino, U. Kähler and F. Sommen, Discrete Dirac operators in Clifford analysis, Adv. Appl. Cliff. Alg., 17 (2007), 451-467. |
[10] |
J. Gilbert and M. Murray, "Clifford Algebra and Dirac Operators in Harmonic Analysis," Cambridge University Press, Cambridge, 1991. |
[11] |
K. Gürlebeck and W. Sprössig, "Quaternionic and Clifford Calculus for Physicists and Engineers," J. Wiley & Sons, Chichester, 1997. |
[12] |
S. Kowalevsky, Zur Theorie der partiellen Differentialgleichung, J. für die Reine und Angew. Mathem., 80 (1875), 1-32. |
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