Year: 2026
Type: preprint
Abstract: For every $α>1$ we construct a finite set $A\subset\mathbb{D}$ such that the zero-based invariant subspace $I_A$ fails the wandering subspace property. Consequently, the Beurling-type theorem holds on the weighted Bergman space $A^2_α$ if and only if $-1<α\le1$, confirming a conjecture of Shimorin. As a further application, we extend the prescribed-curvature construction of Hedenmalm and Perdomo to all $α>1$, thereby replacing the constant $α_0\approx1.04$ in their result by $1$.
Source: arXiv (Cornell University)
Authors: Lin, Zhaopeng, Xu, Shibo, Yu, Tao
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G299512929
OpenAlex ID: W7214957645