环形区域上左可逆算子的Shimorin型解析模型及其应用
A Shimorin-type analytic model on an annulus for left-invertible operators and applications
AI总结：
本文提出一种推广Shimorin模型和Gellar模型的左可逆算子解析模型，证明满足特定条件的左可逆算子可表示为环形或圆盘上再生核Hilbert空间中的乘法算子，并将类似结果推广到复合算子。
摘要：
本文引入并研究了一种新的左可逆算子解析模型，该模型同时推广了Shimorin关于左可逆解析算子的解析模型和Gellar关于双边加权平移的模型。我们证明，满足一定条件的左可逆算子$T$可以建模为环形区域或圆盘上向量值解析函数的再生核Hilbert空间上的乘法算子$\mathscr{M}_z$。对于$\ell^2$空间中的复合算子，也建立了类似的结果。
英文摘要：
A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighted shift is introduced and investigated. We show that a left-invertible operator $T$, which satisfies certain conditions can be modelled as a multiplication operator $\mathscr{M}_z$ on a reproducing kernel Hilbert space of vector-valued analytic functions on an annulus or a disc. A similar result for composition operators in $\ell^2$-spaces is established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
