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Classes of biharmonic polynomials and annihilating differential operators

Duman, Duygu (2011) In Master's Theses in Mathematical Sciences MATM01 20112
Mathematics (Faculty of Sciences)
Abstract
It is well-known that the classical Poisson kernel for the unit disc $\D$ in the complex plane is naturally associated to the Laplacian. In this paper we establish a similar relationship between the kernel $$ P_2(z)=\frac{1}{2}\frac{(1-\lvert z\rvert^2)^3}{\lvert 1-z\rvert^4}, \quad z\in\D,$$ and a certain second order differential operator $D_2(z,\partial)$. The analysis of this relationship depends on careful annihilator considerations based on the Almansi representation of biharmonic functions.
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author
Duman, Duygu
supervisor
organization
course
MATM01 20112
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMA-3064-2011
ISSN
1404-6342
language
English
id
2493467
date added to LUP
2012-09-20 15:47:06
date last changed
2012-09-20 15:47:06
@misc{2493467,
  abstract     = {It is well-known that the classical Poisson kernel for the unit disc $\D$ in the complex plane is naturally associated to the Laplacian. In this paper we establish a similar relationship between the kernel $$ P_2(z)=\frac{1}{2}\frac{(1-\lvert z\rvert^2)^3}{\lvert 1-z\rvert^4}, \quad z\in\D,$$ and a certain second order differential operator $D_2(z,\partial)$. The analysis of this relationship depends on careful annihilator considerations based on the Almansi representation of biharmonic functions.},
  author       = {Duman, Duygu},
  issn         = {1404-6342},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {Classes of biharmonic polynomials and annihilating differential operators},
  year         = {2011},
}