Some automorphism invariance properties for multicontractions

Characteristic functions for multicontractions and automorphisms of the unit ball

A \emph{multicontraction} on a Hilbert space $\HH$ is an $n$-tuple of operators $T=(T_1,...,T_n)$ acting on $\HH$, such that $\sum_{i=1}^n T_i T_i^*\le \1_\HH$. We obtain some results related to the characteristic function of a commuting multicontraction, most notably discussing its behaviour with respect to the action of the analytic automorphisms of the unit ball.

有界对称域上本质正规性的双全纯不变性

The biholomorphic invariance of essential normality on bounded symmetric domains

本文通过新积分公式和代数方法，证明了有界对称域上Hilbert模的p-本质正规性在双全纯映射及自同构乘子下保持不变，并推广了无穷本质正规性与超刚性的等价结果。

Approximation by group invariant subspaces

In this article we study the structure of $Γ$-invariant spaces of $L^2(\bf R)$. Here $\bf R$ is a second countable LCA group. The invariance is with respect to the action of $Γ$, a non commutative group in the form of a semidirect product of a discrete cocompact subgroup of $\bf R$ and a group of automorphisms. This class includes in particular most of the crystallographic groups. We obtain a complete characterization of $Γ$-invariant subspaces in terms of range functions associated to shift-invariant spaces. We also define a new notion of range function adapted to the $Γ$-invariance and const…