tangential vector field
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2018 ◽  
Vol 16 (03) ◽  
pp. 407-433
Author(s):  
Peter Greiner ◽  
Yutian Li

Let [Formula: see text] denote the holomorphic tangential vector field to the generalized upper-half plane [Formula: see text]. In our terminology, [Formula: see text]. Consider the [Formula: see text] operator on the boundary of [Formula: see text], [Formula: see text]; note that [Formula: see text] is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution [Formula: see text] to [Formula: see text]. Our approach is based on special functions and their properties.


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