Exceptional Sets of Slices for Functions From the Bergman Space in the Ball

Canadian mathematical bulletin

关键词: symplectic manifold;    Lagrangian foliation;    affine connection;   

DOI  :  10.4153/CMB-2001-019-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $B_N$ be the unit ball in $mathbb{C}^N$ and let $f$ be a functionholomorphic and $L^2$-integrable in $B_N$. Denote by $E(B_N,f)$the set of all slices of the form $Pi =Lcap B_N$, where $L$ is acomplex one-dimensional subspace of $mathbb{C}^N$, for which $f|_{Pi}$is not $L^2$-integrable (with respect to the Lebesgue measure on $L$).Call this set the exceptional set for $f$. We give a characterizationof exceptional sets which are closed in the natural topology of slices.

【 授权许可】

Unknown