A fundamental solution for a nonelliptic partial differential operator, II

Peter Greiner; Yutian Li

doi:10.1142/S0219530516500196

A fundamental solution for a nonelliptic partial differential operator, II

Peter Greiner^*, Yutian Li

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

1 Citation (Scopus)

Abstract

Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ²; Ρ = Im z 1 -|z|⁴ > 0}. In our terminology, t = Re z₁. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.

Original language	English
Pages (from-to)	407-433
Number of pages	27
Journal	Analysis and Applications
Volume	16
Issue number	3
DOIs	https://doi.org/10.1142/S0219530516500196
Publication status	Published - 1 May 2018

Scopus Subject Areas

Analysis
Applied Mathematics

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fundamental solution
special functions
Subelliptic operator

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10.1142/S0219530516500196

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title = "A fundamental solution for a nonelliptic partial differential operator, II",

abstract = "Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ2; Ρ = Im z 1 -|z|4 > 0}. In our terminology, t = Re z1. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.",

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AU - Greiner, Peter

AU - Li, Yutian

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ2; Ρ = Im z 1 -|z|4 > 0}. In our terminology, t = Re z1. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.

AB - Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ2; Ρ = Im z 1 -|z|4 > 0}. In our terminology, t = Re z1. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.

KW - fundamental solution

KW - special functions

KW - Subelliptic operator

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EP - 433

JO - Analysis and Applications

JF - Analysis and Applications

IS - 3

ER -

A fundamental solution for a nonelliptic partial differential operator, II

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