Geodesic
A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 795-808 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis.
Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis.
DOI : 10.21136/CMJ.2017.0187-16
Classification : 26B20, 30G35, 58C50
Keywords: super Dunkl-Dirac operator; Stokes formula; Cauchy-Pompeiu integral formula; Morera's theorem; Painlevé theorem 
@article{10_21136_CMJ_2017_0187_16,
     author = {Yuan, Hongfen},
     title = {A {Cauchy-Pompeiu} formula in super {Dunkl-Clifford} analysis},
     journal = {Czechoslovak Mathematical Journal},
     pages = {795--808},
     year = {2017},
     volume = {67},
     number = {3},
     doi = {10.21136/CMJ.2017.0187-16},
     mrnumber = {3697917},
     zbl = {06770131},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0187-16/}
}
TY  - JOUR
AU  - Yuan, Hongfen
TI  - A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis
JO  - Czechoslovak Mathematical Journal
PY  - 2017
SP  - 795
EP  - 808
VL  - 67
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0187-16/
DO  - 10.21136/CMJ.2017.0187-16
LA  - en
ID  - 10_21136_CMJ_2017_0187_16
ER  - 
%0 Journal Article
%A Yuan, Hongfen
%T A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis
%J Czechoslovak Mathematical Journal
%D 2017
%P 795-808
%V 67
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0187-16/
%R 10.21136/CMJ.2017.0187-16
%G en
%F 10_21136_CMJ_2017_0187_16
Yuan, Hongfen. A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 795-808. doi: 10.21136/CMJ.2017.0187-16

[1] Bernardes, G., Cerejeiras, P., Kähler, U.: Fischer decomposition and Cauchy kernel for Dunkl-Dirac operators. Adv. Appl. Clifford Algebr. 19 (2009), 163-171. | DOI | MR | JFM

[2] Cerejeiras, P., Kähler, U., Ren, G.: Clifford analysis for finite reflection groups. Complex Var. Elliptic Equ. 51 (2006), 487-495. | DOI | MR | JFM

[3] Coulembier, K., Bie, H. De, Sommen, F.: Integration in superspace using distribution theory. J. Phys. A, Math. Theor. 42 (2009), Article ID 395206, 23 pages. | DOI | MR | JFM

[4] Bie, H. De, Schepper, N. De: Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator. Bull. Belg. Math. Soc.-Simon Stevin 18 (2011), 193-214. | DOI | MR | JFM

[5] Bie, H. De, Sommen, F.: Correct rules for Clifford calculus on superspace. Adv. Appl. Clifford Algebr. 17 (2007), 357-382. | DOI | MR | JFM

[6] Bie, H. De, Sommen, F.: Spherical harmonics and integration in superspace. J. Phys. A, Math. Theor. 40 (2007), 7193-7212. | DOI | MR | JFM

[7] Dunkl, C. F.: Differential-difference operators associated to reflection groups. Trans. Am. Math. Soc. 311 (1989), 167-183. | DOI | MR | JFM

[8] Dunkl, C. F., Xu, Y.: Orthogonal Polynomials of Several Variables. Encyclopedia of Mathematics and Its Applications 81, Cambridge University Press, Cambridge (2001). | DOI | MR | JFM

[9] Fei, M. G.: Fundamental solutions of iterated Dunkl-Dirac operators and their applications. Acta Math. Sci. Ser. A, Chin. Ed. 33 (2013), 1052-1061 Chinese. | MR | JFM

[10] Fei, M., Cerejeiras, P., Kähler, U.: Fueter's theorem and its generalizations in Dunkl-Clifford analysis. J. Phys. A, Math. Theor. 42 (2009), Article ID 395209, 15 pages. | DOI | MR | JFM

[11] Fei, M., Cerejeiras, P., Kähler, U.: Spherical Dunkl-monogenics and a factorization of the Dunkl-Laplacian. J. Phys. A, Math. Theor. 43 (2010), Article ID 445202, 14 pages. | DOI | MR | JFM

[12] Heckman, G. J.: Dunkl operators. Séminaire Bourbaki, Volume 1996/97. Exposés 820-834. Société Mathématique de France, Astérisque 245 (1997), 223-246. | MR | JFM

[13] Humphreys, J. E.: Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, Cambridge (1990). | DOI | MR | JFM

[14] Ren, G.: Howe duality in Dunkl superspace. Sci. China, Math. 53 (2010), 3153-3162. | DOI | MR | JFM

[15] Trimèche, K.: Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators. Integral Transforms Spec. Funct. 13 (2002), 17-38. | DOI | MR | JFM

[16] Diejen, J. F. Van, (eds.), L. Vinet: Calogero-Moser-Sutherland Models. Workshop, Centre de Recherches Mathématique, Montréal, 1997. CRM Series in Mathematical Physics, Springer, New York (2000). | DOI | MR | JFM

[17] Yuan, H. F., Karachik, V. V.: Dunkl-Poisson equation and related equations in superspace. Math. Model. Anal. 20 (2015), 768-781. | DOI | MR

[18] Yuan, H., Qiao, Y., Yang, H.: Properties of $k$-monogenic functions and their relative functions in superspace. Adv. Math., Beijing 42 (2013), 233-242 Chinese. | MR | JFM

[19] Yuan, H., Zhang, Z., Qiao, Y.: Polynomial Dirac operators in superspace. Adv. Appl. Clifford Algebr. 25 (2015), 755-769. | DOI | MR | JFM

Cité par Sources :