On the Radial Part of the Cauchy-Riemann Operator

2000 ◽  
pp. 261-271
Author(s):  
Thomas Hempfling
Keyword(s):  
Radial Part ◽  
Cauchy Riemann

SOME BOUNDARY VALUE PROBLEMS FOR THE CAUCHY-RIEMANN EQUATION IN HALF LENS

2018 ◽  
Vol 9 (3) ◽  
pp. 73-84
Author(s):  
N. Taghizadeh ◽  
◽  
V. Soltani Mohammadi ◽  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Riemann Equation ◽  
Cauchy Riemann

scholarly journals On Symmetric Cauchy–Riemann Manifolds

2000 ◽  
Vol 149 (2) ◽  
pp. 145-181 ◽  
Author(s):  
Wilhelm Kaup ◽  
Dmitri Zaitsev
Keyword(s):  
Riemann Manifolds ◽  
Cauchy Riemann

Hypoellipticity in the tangential Cauchy-Riemann complex

1994 ◽  
Vol 73 (1) ◽  
pp. 25-77
Author(s):  
G�bor Francsics
Keyword(s):  
Cauchy Riemann

scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (1) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

scholarly journals Factoring analytic multivariate polynomials and non-standard Cauchy–Riemann conditions

2014 ◽  
Vol 104 ◽  
pp. 43-57 ◽  
Author(s):  
Tomas Recio ◽  
J.-Rafael Sendra ◽  
Luis-Felipe Tabera ◽  
Carlos Villarino
Keyword(s):  
Multivariate Polynomials ◽  
Cauchy Riemann
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