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 Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tommaso Rossi
Keyword(s):  
Heisenberg Group ◽  
Mean Curvature ◽  
Smooth Surface ◽  
Characteristic Point ◽  
Analytic Surface ◽  
Characteristic Set ◽  
Characteristic Points ◽  
The Mean ◽  
Real Analytic ◽  
Real Analytic Surface

Abstract We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this paper is the introduction of a concept of a mildly degenerate characteristic point for a smooth surface of the Heisenberg group, in a neighborhood of which the sub-Riemannian mean curvature is integrable (with respect to the perimeter measure induced by the Euclidean structure). As a consequence, we partially answer to a question posed by Danielli, Garofalo and Nhieu in [D. Danielli, N. Garofalo and D. M. Nhieu, Integrability of the sub-Riemannian mean curvature of surfaces in the Heisenberg group, Proc. Amer. Math. Soc. 140 2012, 3, 811–821], proving that the mean curvature of a real-analytic surface with discrete characteristic set is locally integrable.

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
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