0
votes
0answers
67 views

Invertibility of Paneitz operator on a compact manifold without boundary

Let $(M,g)$ be a Riemannian manifold of any even dimension that we assume compact and without boundary and $P_g$ the Paneitz operator in the metric $g$. The question is the following: how to define a ...
2
votes
1answer
212 views

hayman's result for $ A^2(D) $

Consider injective homolomorphic functions $f:\mathbb D\to \mathbb C$ on the unit disk $|z|\leq 1$, normalized by the conditions $f(0)=0$ and $f'(0)=1$. Thus for $|z|\leq 1$ we have $ ...
1
vote
2answers
355 views

Conformal transformations and harmonic analysis on the sphere

Consider the $n$-dimensional sphere $S^n$. I'm especially interested in the $n=4$ case. The Hilbert space $L^2(S^n)$ can be decomposed into a direct sum of eigenspaces of the Laplacian, which are ...