Classes of biharmonic polynomials and annihilating differential operators
(2011) In Master's Theses in Mathematical Sciences MATM01 20112Mathematics (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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/2493467
- author
- Duman, Duygu
- supervisor
- organization
- course
- MATM01 20112
- year
- 2011
- 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}}, }