  We describe the locally analytic $\mathrm{GL}_d(K)$-representations which
arise as the global sections of homogeneous vector bundles on the projective
space restricted to the Drinfeld upper half space over a non-archimedean local
field $K$. We thereby generalize work of Orlik (2008) for $p$-adic fields to
the effect that it becomes applicable to local fields of positive
characteristic. Our description of this space of global sections is in terms of
a filtration by subrepresentations, and a characterization of the resulting
subquotients via adaptations of the functors $\mathcal{F}^G_P$ considered by
Orlik-Strauch (2015) and Agrawal-Strauch (2022). For a local field $K$ of
positive characteristic, we also determine the locally analytic (resp.
continuous) characters of $K^\times$ with values in $K$-Banach algebras which
are integral domains (resp. with values in finite extensions of $K$) in an
appendix.
