论文标题
塑态功能的Banach空间上的加权组成半群
Weighted composition semigroups on Banach spaces of holomorphic functions
论文作者
论文摘要
我们研究某些Banach空间$ x $，是加权构图运营商的家族。值得注意的是，我们表明，如果这个家族形成强烈连续的半群，则其无限发电机（$γ，d（γ）$）由$γf= gf+gf+gf+gf^\ prime prime $ d（γ）= \ {f \ in x \ | \ gf+gf^\ prime \ in x \} $，其中$ g，g $是holomorphic函数。此外，我们的第二个MAIM结果是研究互惠的含义。那就是$（γ，d（γ））$，如上所述，产生了一个强烈的连续半群，那么这是一个加权组成算子的家族。
We study, to certain Banach spaces $X$, families of weighted composition operators. Notably, we show that if this family form a strongly continuous semigroup, then its infinitesimal generator ($Γ, D(Γ)$) is given by $Γf = gf+Gf^\prime$ with $D(Γ) = \{ f\in X \ | \ gf+Gf^\prime\in X \}$ where $g, G$ are holomorphic functions. Moreover, our second maim result is to study the reciprocal implication. That is if $(Γ, D(Γ))$, define like above, generate a strongly continuous semigroup, then this one is a family of weighted composition operators.
