4 problems

Let $M$ be an open manifold with nonnegative Ricci curvature, and consider the vector space of biharmonic functions on $M$, where biharmonic means satisfying … For a fixed growth r…

Let $M$ be an open manifold with nonnegative Ricci curvature, and let $u$ be a bounded biharmonic function on $M$, meaning that $abla^4 u=0$ in the source's terminology via the bi…

For $n>1$, let $p,q\in{\mathbb C}^{n+1}$, and let $\pi_n$ be the $(n+1)$-dimensional irreducible representation of $\mathrm{SU}(2)$. For fixed indices $\alpha$ and $\beta$, define…

Let $\gamma$ be a non-negative integer, and let $F_\gamma$ be the Poisson kernel under consideration. For $1\leq\beta\leq\gamma+2$, let $f_\beta(x)$ be polynomials. Explicit…