scholarly journals Another Type of Cauchy's Integral Formula in Complex Clifford Analysis

1997 ◽  
Vol 20 (1) ◽  
pp. 187-204 ◽  
Author(s):  
Kimirô SANO
Keyword(s):  
Clifford Analysis ◽  
Integral Formula ◽  
Cauchy’S Integral Formula

scholarly journals Complex Clifford analysis and domains of holomorphy

1990 ◽  
Vol 48 (3) ◽  
pp. 413-433 ◽  
Author(s):  
John Ryan
Keyword(s):  
Clifford Analysis ◽  
Integral Formula ◽  
Complex Variables ◽  
Analytic Surface ◽  
Higher Dimension ◽  
Cauchy’S Integral Formula ◽  
Domains Of Holomorphy ◽  
Huygens Principle ◽  
Real Analytic ◽  
Real Analytic Surface

AbstractIntegrals related to Cauchy's integral formula and Huygens' principle are used to establish a link between domains of holomorphy in n complex variables and cells of harmonicity in one higher dimension. These integrals enable us to determine domains to which analytic functions on real analytic surface in Rn+1 may be extended to solutions to a Dirac equation.

scholarly journals Meromorphic or Holomorphic Completion of a Reinhardt Domain

1970 ◽  
Vol 38 ◽  
pp. 1-12 ◽  
Author(s):  
Eiichi Sakai
Keyword(s):  
Meromorphic Function ◽  
Power Series ◽  
Meromorphic Functions ◽  
Integral Formula ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Reinhardt Domain ◽  
Continuity Theorem ◽  
Cauchy’S Integral Formula ◽  
Long Time

In the theory of functions of several complex variables, the problem about the continuation of meromorphic functions has not been much investigated for a long time in spite of its importance except the deeper result of the continuity theorem due to E. E. Levi [4] and H. Kneser [3], The difficulty of its investigation is based on the following reasons: we can not use the tools of not only Cauchy’s integral formula but also the power series and there are indetermination points for the meromorphic function of many variables different from one variable. Therefore we shall also follow the Levi and Kneser’s method and seek for the aspect of meromorphic completion of a Reinhardt domain in Cn.

scholarly journals On the Surface Fields of a Small Circular Loop Antenna Placed on Plane Stratified Earth

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mauro Parise
Keyword(s):  
Analytical Method ◽  
Integral Formula ◽  
Integral Representations ◽  
Loop Antenna ◽  
Circular Loop ◽  
Time Harmonic ◽  
Hankel Functions ◽  
Cauchy’S Integral Formula ◽  
Em Field ◽  
Surface Fields

An analytical method is presented which makes it possible to derive exact explicit expressions for the time-harmonic surface fields excited by a small circular loop antenna placed on the top surface of plane layered earth. The developed procedure leads to casting the complete integral representations for the EM field components into forms suitable for application of Cauchy’s integral formula. As a result, the surface fields are expressed as sums of Hankel functions. Numerical simulations are performed to show the validity and accuracy of the proposed solution.

Cauchy’s Integral Formula

2011 ◽  
pp. 111-115
Author(s):  
Ravi P. Agarwal ◽  
Kanishka Perera ◽  
Sandra Pinelas
Keyword(s):  
Integral Formula ◽  
Cauchy’S Integral Formula

A Cauchy Integral Formula for Infrapolymonogenic Functions in Clifford Analysis

2020 ◽  
Vol 30 (2) ◽  
Author(s):  
Ricardo Abreu Blaya ◽  
Juan Bory Reyes ◽  
Arsenio Moreno García ◽  
Tania Moreno García
Keyword(s):  
Clifford Analysis ◽  
Integral Formula ◽  
Cauchy Integral Formula ◽  
Cauchy Integral

On convergence and quasiconformality of complex planar spline interpolants

1986 ◽  
Vol 99 (2) ◽  
pp. 347-356 ◽  
Author(s):  
H. P. Dikshit ◽  
A. Ojha
Keyword(s):  
Finite Elements ◽  
Integral Formula ◽  
Holomorphic Functions ◽  
The Other ◽  
Piecewise Function ◽  
Cauchy’S Integral Formula ◽  
Recent Origin ◽  
Image Position ◽  
Spline Interpolants ◽  
Identity Theorem

There appear to be two main approaches for developing complex splines. One of these, which has been in use for quite some time, consists in defining splines on the boundary of a given region which are then extended into the interior by Cauchy's integral formula (see e.g. [1]). The other approach, which is of a more recent origin, is motivated in spirit by the theory of finite elements (see e.g. [10], p. 320) and is contained in [8] and [9]. Observing that the foregoing extension into the interior is not easy to execute numerically, certain continuous piecewise non-holomorphic functions, called complex planar splines have been studied in [8] and [9]. The choice of non-holomorphic functions is justified, since if we take the pieces to be holomorphic functions like polynomials, then by the well known identity theorem ([5], p. 132, theorem 60) the continuity of such a piecewise function implies that all the pieces represent just one holomorphic function. Thus, we shall consider polynomials in z and its conjugate z¯ of the formwhich are generally non-holomorphic functions. The numberwill be called the degree of q. For simplicity we also write q(z) for q(z, z¯).

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