A laurent expansion and residue theorems of k-regular functions in clifford analysis

2009 ◽  
Vol 14 (2) ◽  
pp. 97-102 ◽  
Author(s):  
Min Ku ◽  
Jinyuan Du
Keyword(s):  
Clifford Analysis ◽  
Laurent Expansion ◽  
Regular Functions

scholarly journals SEVERAL PROPERTIES OF QUATERNIONIC REGULAR FUNCTIONS IN CLIFFORD ANALYSIS

2015 ◽  
Vol 37 (4) ◽  
pp. 569-575 ◽  
Author(s):  
HAN UL KANG ◽  
MIN JI KIM ◽  
KWANG HO SHON
Keyword(s):  
Clifford Analysis ◽  
Regular Functions

scholarly journals Regular functions with values in a noncommutative algebra using Clifford analysis

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1747-1755
Author(s):  
Su Lim ◽  
Kwang Shon
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Clifford Analysis ◽  
Regular Function ◽  
Complex Variables ◽  
Partial Differential ◽  
Noncommutative Algebra ◽  
Regular Functions ◽  
Commutative Subalgebra ◽  
Pauli Matrices

We construct a noncommutative algebra C(2) that is a subalgebra of the Pauli matrices of M(2;C), and investigate the properties of solutions with values in C(2) of the inhomogeneous Cauchy-Riemann system of partial differential equations with coefficients in the associated Pauli matrices. In addition, we construct a commutative subalgebra C(4) of M(4;C), obtain some properties of biregular functions with values in C(2) on in C2 x C2, define a J-regular function of four complex variables with values in C(4), and examine some properties of J-regular functions of partial differential equations.

scholarly journals The Boundary Value Problem with Haseman-shift for k-regular Functions on Unbounded Domains in Clifford Analysis

2016 ◽  
Vol 8 (1) ◽  
pp. 38
Author(s):  
Yan Zhang
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Unique Solution ◽  
Clifford Analysis ◽  
Boundary Value ◽  
Regular Function ◽  
Unbounded Domains ◽  
Regular Functions

In this paper, we introduce the boundary value problem with Haseman shift for $k$-regular function on unbounded domains, and give the unique solution for this problem by integral equation<br />method and fixed-point theorem.

scholarly journals Hilbert series associated to symplectic quotients by SU2

2020 ◽  
Vol 30 (07) ◽  
pp. 1323-1357
Author(s):  
Hans-Christian Herbig ◽  
Daniel Herden ◽  
Christopher Seaton
Keyword(s):  
Explicit Expression ◽  
Hilbert Series ◽  
Laurent Expansion ◽  
Graded Algebra ◽  
Regular Functions ◽  
Nonzero Coefficient ◽  
Symplectic Quotients ◽  
The Way

We compute the Hilbert series of the graded algebra of real regular functions on the symplectic quotient associated to an [Formula: see text]-module and give an explicit expression for the first nonzero coefficient of the Laurent expansion of the Hilbert series at [Formula: see text]. Our expression for the Hilbert series indicates an algorithm to compute it, and we give the output of this algorithm for all representations of dimension at most [Formula: see text]. Along the way, we compute the Hilbert series of the module of covariants of an arbitrary [Formula: see text]- or [Formula: see text]-module as well as its first three Laurent coefficients.

The Left Hilbert BVP for h-Regular Functions in Clifford Analysis

2012 ◽  
Vol 23 (2) ◽  
pp. 519-533
Author(s):  
Si Zhongwei ◽  
Du Jinyuan ◽  
Duan Ping
Keyword(s):  
Clifford Analysis ◽  
Regular Functions

scholarly journals Linear BVPs and SIEs for Generalized Regular Functions in Clifford Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Pingrun Li ◽  
Lixia Cao
Keyword(s):  
Clifford Analysis ◽  
Complex Analysis ◽  
Boundary Value ◽  
Regular Function ◽  
Singular Integral Equations ◽  
Value Theory ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Regular Functions ◽  
Plemelj Formula

We study some properties of a regular function in Clifford analysis and generalize Liouville theorem and Plemelj formula with values in Clifford algebra An(R). By means of the classical Riemann boundary value problem and of the theory of a regular function, we discuss some boundary value problems and singular integral equations in Clifford analysis and obtain the explicit solutions and the conditions of solvability. Thus, the results in this paper will be of great significance for the study of improving and developing complex analysis, integral equation, and boundary value theory.

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