Mathematical Sciences

Lund University

  • Title: Classes of biharmonic polynomials and annihilating differential operators
  • Description: 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.
  • Start Date: Sept. 15, 2011
  • Finished Date: Sept. 15, 2011
  • Supervisor: Anders Olofsson
  • Student: Duygu Duman