Classes of biharmonic polynomials and annihilating differential operators
(2011) In Master's Theses in Mathematical Sciences MATM01 20112Mathematics (Faculty of Sciences)
 Abstract
 It is wellknown 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 $$ P_2(z)=\frac{1}{2}\frac{(1\lvert z\rvert^2)^3}{\lvert 1z\rvert^4}, \quad z\in\D,$$ 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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/2493467
 author
 Duman, Duygu
 supervisor

 Anders Olofsson ^{LU}
 organization
 course
 MATM01 20112
 year
 2011
 type
 H2  Master's Degree (Two Years)
 subject
 publication/series
 Master's Theses in Mathematical Sciences
 report number
 LUNFMA30642011
 ISSN
 14046342
 language
 English
 id
 2493467
 date added to LUP
 20120920 15:47:06
 date last changed
 20120920 15:47:06
@misc{2493467, abstract = {It is wellknown 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 $$ P_2(z)=\frac{1}{2}\frac{(1\lvert z\rvert^2)^3}{\lvert 1z\rvert^4}, \quad z\in\D,$$ 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 = {14046342}, language = {eng}, note = {Student Paper}, series = {Master's Theses in Mathematical Sciences}, title = {Classes of biharmonic polynomials and annihilating differential operators}, year = {2011}, }