| Title:
|
A Cauchy-Pompeiu formula in super Dunkl-Clifford analysis (English) |
| Author:
|
Yuan, Hongfen |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
795-808 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
super Dunkl-Dirac operator |
| Keyword:
|
Stokes formula |
| Keyword:
|
Cauchy-Pompeiu integral formula |
| Keyword:
|
Morera's theorem |
| Keyword:
|
Painlevé theorem |
| MSC:
|
26B20 |
| MSC:
|
30G35 |
| MSC:
|
58C50 |
| idZBL:
|
Zbl 06770131 |
| idMR:
|
MR3697917 |
| DOI:
|
10.21136/CMJ.2017.0187-16 |
| . |
| Date available:
|
2017-09-01T12:25:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146860 |
| . |
| Reference:
|
[1] Bernardes, G., Cerejeiras, P., Kähler, U.: Fischer decomposition and Cauchy kernel for Dunkl-Dirac operators.Adv. Appl. Clifford Algebr. 19 (2009), 163-171. Zbl 1172.30020, MR 2524663, 10.1007/s00006-009-0151-x |
| Reference:
|
[2] Cerejeiras, P., Kähler, U., Ren, G.: Clifford analysis for finite reflection groups.Complex Var. Elliptic Equ. 51 (2006), 487-495. Zbl 1115.30053, MR 2230262, 10.1080/17476930500482499 |
| Reference:
|
[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. Zbl 1187.58011, MR 2539324, 10.1088/1751-8113/42/39/395206 |
| Reference:
|
[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. Zbl 1227.30038, MR 2847756, 10.36045/bbms/1307452070 |
| Reference:
|
[5] Bie, H. De, Sommen, F.: Correct rules for Clifford calculus on superspace.Adv. Appl. Clifford Algebr. 17 (2007), 357-382. Zbl 1129.30034, MR 2350585, 10.1007/s00006-007-0042-y |
| Reference:
|
[6] Bie, H. De, Sommen, F.: Spherical harmonics and integration in superspace.J. Phys. A, Math. Theor. 40 (2007), 7193-7212. Zbl 1143.30315, MR 2344451, 10.1088/1751-8113/40/26/007 |
| Reference:
|
[7] Dunkl, C. F.: Differential-difference operators associated to reflection groups.Trans. Am. Math. Soc. 311 (1989), 167-183. Zbl 0652.33004, MR 0951883, 10.2307/2001022 |
| Reference:
|
[8] Dunkl, C. F., Xu, Y.: Orthogonal Polynomials of Several Variables.Encyclopedia of Mathematics and Its Applications 81, Cambridge University Press, Cambridge (2001). Zbl 0964.33001, MR 1827871, 10.1017/CBO9780511565717 |
| Reference:
|
[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. Zbl 1313.33013, MR 3184906 |
| Reference:
|
[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. Zbl 1230.30033, MR 2539327, 10.1088/1751-8113/42/39/395209 |
| Reference:
|
[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. Zbl 1203.30054, MR 2733821, 10.1088/1751-8113/43/44/445202 |
| Reference:
|
[12] Heckman, G. J.: Dunkl operators.Séminaire Bourbaki, Volume 1996/97. Exposés 820-834. Société Mathématique de France, Astérisque 245 (1997), 223-246. Zbl 0916.33012, MR 1627113 |
| Reference:
|
[13] Humphreys, J. E.: Reflection Groups and Coxeter Groups.Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, Cambridge (1990). Zbl 0725.20028, MR 1066460, 10.1017/CBO9780511623646 |
| Reference:
|
[14] Ren, G.: Howe duality in Dunkl superspace.Sci. China, Math. 53 (2010), 3153-3162. Zbl 1213.30087, MR 2746313, 10.1007/s11425-010-4063-y |
| Reference:
|
[15] Trimèche, K.: Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators.Integral Transforms Spec. Funct. 13 (2002), 17-38. Zbl 1030.44004, MR 1914125, 10.1080/10652460212888 |
| Reference:
|
[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). Zbl 0942.00063, MR 1843558, 10.1007/978-1-4612-1206-5 |
| Reference:
|
[17] Yuan, H. F., Karachik, V. V.: Dunkl-Poisson equation and related equations in superspace.Math. Model. Anal. 20 (2015), 768-781. MR 3427166, 10.3846/13926292.2015.1112856 |
| Reference:
|
[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. Zbl 1299.30132, MR 3112909 |
| Reference:
|
[19] Yuan, H., Zhang, Z., Qiao, Y.: Polynomial Dirac operators in superspace.Adv. Appl. Clifford Algebr. 25 (2015), 755-769. Zbl 1325.35008, MR 3384860, 10.1007/s00006-014-0524-7 |
| . |
