A Survey on the (Hyper-) Derivatives in Complex, Quaternionic and Clifford Analysis

被引：21

作者：

Luna-Elizarraras, M. E. ^{[1
]}

Shapiro, M. ^{[1
]}

机构：

[1] Inst Politecn Nacl, Escuela Super Fis & Matemat, Mexico City 07338, DF, Mexico

来源：

MILAN JOURNAL OF MATHEMATICS | 2011年 / 79卷 / 02期

关键词：

Quaternionic analysis; Clifford analysis; hyperderivative;

D O I：

10.1007/s00032-011-0169-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The complex derivative serves as one of the definitions for holomorphic functions but also as an important characteristic of the latter having algebraic, topologic and analytic aspects. The goal of the paper is to explain that in the framework of quaternionic and Clifford analyses there exists the hyperderivative of a hyperholomorphic function which extends to the corresponding situations a series of fundamental properties of its complex antecedent.

引用

页码：521 / 542

页数：22

共 12 条

[1] A Survey on the (Hyper-) Derivatives in Complex, Quaternionic and Clifford Analysis
M. E. Luna-Elizarrarás
M. Shapiro
Milan Journal of Mathematics, 2011, 79 : 521 - 542
[2] A POLAR REPRESENTATION OF A REGULARITY OF A DUAL QUATERNIONIC FUNCTION IN CLIFFORD ANALYSIS
Kim, Ji Eun
Shon, Kwang Ho
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (02) : 583 - 592
[3] DOMAINS OF HYPERHOLOMORPHY AND HYPER STEIN DOMAINS ON CLIFFORD ANALYSIS
Park, Hee Young
Shon, Kwang Ho
JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2007, 14 (02): : 91 - 98
[4] The corresponding inverse of functions of multidual complex variables in Clifford analysis
Kim, Ji Eun
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (06): : 4520 - 4528
[5] Compound Riemann Hilbert Boundary Value Problems in Complex and Quaternionic Analysis
Bory Reyes, Juan
Tamayo Castro, Carlos Daniel
Abreu Blaya, Ricardo
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2017, 27 (02) : 977 - 991
[6] Compound Riemann Hilbert Boundary Value Problems in Complex and Quaternionic Analysis
Juan Bory Reyes
Carlos Daniel Tamayo Castro
Ricardo Abreu Blaya
Advances in Applied Clifford Algebras, 2017, 27 : 977 - 991
[7] Cauchy type integrals and a boundary value problem in a complex Clifford analysis
Nanbin Cao
Zunfeng Li
Heju Yang
Yuying Qiao
Acta Mathematica Scientia, 2024, 44 : 369 - 385
[8] Cauchy type integrals and a boundary value problem in a complex Clifford analysis
Cao, Nanbin
Li, Zunfeng
Yang, Heju
Qiao, Yuying
ACTA MATHEMATICA SCIENTIA, 2024, 44 (01) : 369 - 385
[9] Dirichlet-Type Problems for the Two-Dimensional Helmholtz Operator in Complex Quaternionic Analysis
Bory-Reyes, Juan
Abreu-Blaya, Ricardo
Hernandez-Simon, Luis M.
Schneider, Baruch
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (06) : 4901 - 4916
[10] Higher Order Dirichlet-Type Problems in 2D Complex Quaternionic Analysis
Schneider, B.
VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS, 2019, 52 (04) : 409 - 418

← 1 2 →