본문 바로가기
KERD
논문KCI 등재

Riquier and Dirichlet boundary value problems for slice Dirac operators

Hongfen Yuan
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회보 (Bulletin of the KMS)|제55권 제1호|pp. 149-163

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

Euler operatorDirichlet problemslice Dirac operatorgeneralized slice Dirac operatorRiquier problem
주제분류수학

초록

In recent years, the study of slice Dirac operators has attracted more and more attention in the literature. In this paper, Almansi-type decompositions for null solutions to the iterated slice Dirac operator and the generalized slice Dirac operator are obtained without a star-like domain centered at the origin. As applications, we investigate Riquier type problems and Dirichlet type problems in the theory of slice monogenic functions.

Abstract

In recent years, the study of slice Dirac operators has attracted more and more attention in the literature. In this paper, Almansi-type decompositions for null solutions to the iterated slice Dirac operator and the generalized slice Dirac operator are obtained without a star-like domain centered at the origin. As applications, we investigate Riquier type problems and Dirichlet type problems in the theory of slice monogenic functions.

참고문헌 (19)

  1. E. Almansi, "Sullintegrazione dellequazione differenziale <TEX>${\Delta}^{2m}u=0$<", TEX>, 1899, pp.2(3), 1~51
  2. N. Aronszajn, "Polyharmonic functions, Oxford Mathematics Monographs" (1983), The Clarendon Press, Oxford University Press
  3. F. Brackx, "Clifford Analysis, Pitman Research Notes in Mathematics Series, vol. 76" (1982), Pitman
  4. L. Cnudde, "Algebraic approach to Slice Monogenic functions", Complex Anal. Oper. Theory, 9(5), pp.1065~1087 (2015)[DOI]
  5. F. Colombo, "Slice monogenic functions", Isr. J. Math., 171, pp.385~403 (2009)[DOI]
  6. F. Colombo, "An extension theorem for slice monogenic functions and some of its consequences", Israel J. Math., 177, pp.369~389 (2010)[DOI]
  7. F. Colombo, "The Runge theorem for slice hyperholomorphic functions", Proc. Amer. Math. Soc., 139(5), pp.1787~1803 (2011)[DOI]
  8. H. De Bie, "Dunkl operators and a family of realizations of osp(<TEX>$1{\mid}2$<", TEX>), 2012, pp.364(7), 3875~3902
  9. P. G. L. Dirichlet, "Abh. Koniglich", Preuss. Akad. Wiss., pp.99~116 (1850)
  10. G. Gentili, "Advances in Hypercomplex Analysis, Springer INdAM Series, vol. 1" (2013), Springer
  11. G. Gentili, "A new theory of regular functions of a quaternionic variable", Adv. Math., 216(1), pp.279~301 (2007)[DOI]
  12. F. L. He, "Riemann-Hilbert problems for null-solutions to iterated generalized Cauchy-Riemann equations in axially symmetric domains", Computers and Mathematics with Applications, 71(10), pp.1990~2000 (2016)[DOI]
  13. V. V. Karachik, "Normalized system of functions with respect to the Laplace operator and its applications", J. Math. Anal. Appl., 287(2), pp.577~592 (2003)[DOI]
  14. H. Malonek, "Almansi-type theorems in Clifford analysis", Math. Methods Appl. Sci., 25(16-18), pp.1541~1552 (2002)[DOI]
  15. M. Nicolescu, "Les Fonctions Polyharmoniques" (1936), Hermann
  16. H. F. Yuan, "Dirichlet type problems for Dunkl-Poisson equations", Bound. Value Probl., 2016(222), pp.1~16 (2016)[DOI]
  17. H. F. Yuan, "Solutions of the Poisson equation and related equations in super spinor space", Comput. Methods Funct. Theory, 16(4), pp.699~715 (2016)[DOI]
  18. H. F. Yuan, "Solutions of the Dirac and related equations in superspace", Complex Var. Elliptic Equ., 59(9), pp.1315~1327 (2014)[DOI]
  19. H. F. Yuan, "Normalized system for the super Laplace operator", Adv. Appl. Clifford Algebras, 22(4), pp.1109~1128 (2012)[DOI]

관련 논문AI추천

On the Lu Qi-Keng problem for slice monogenic functionsZhenghua Xu대한수학회 · 대한수학회보2018 · 제55권 제5호Szeg\"{o} projections for Hardy spaces in quaternionic Clifford analysisFuli He, Min Ku, Song Huang대한수학회 · 대한수학회보2022 · 제59권 제5호Hypermeromorphy of functions on split quaternions in Clifford analysis김지은, 손광호영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호On the transformation formula of the slice Bergman kernels in the quaternion variablesJong-Do Park대한수학회 · 대한수학회보2016 · 제53권 제5호Conic regular functions of conic quaternion variables in the sense of Clifford analysis김지은, 손광호영남수학회 · East Asian Mathematical Journal2015 · 제31권 제1호Split hyperholomorphic function in Clifford analysis손광호, 임수진한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제1호

이 간행물의 다른 논문 (21건)

A geometric inequality on a compact domain in $\mathbb R^{n}$조용승, 채영도pp. 1-8Operator fractional Brownian sheet and martingale differencesLiangwen Xia, Hongshuai Dai, Guangjun Shenpp. 9-23A structure of noncentral idempotentsZhelin Piao, 조은경, 이양, 곽태근, 서연숙pp. 25-40Multiplication operators on Bergman spaces over polydisks associated with integer matrixHansong Huang, Hui Danpp. 41-50On some special difference equations of Malmquist typeZhang Jiepp. 51-61
원문 보기