AI 中文总结
该研究针对模长≤1的β自守解析函数w，构建了依赖任意特征α的自守de Branges-Rovnyak空间族，通过格林函数乘运算定义酉算子，将其应用于Nevanlinna-Pick问题以扩展等距算子族。
AI 中文摘要
针对模长不超过1的β自守解析函数w，关联了一族依赖任意特征α的自守de Branges-Rovnyak空间。乘格林函数的运算定义了作用于这些空间的酉算子，函数w可作为特征函数从这些算子中恢复。研究表明，对于Nevanlinna-Pick问题，该族酉算子扩展了由插值数据定义的等距算子族。
英文摘要
A family of automorphic de Branges - Rovnyak spaces (depending on an arbitrary character $α$) is associated to a $β$-automorphic analytic function $w$ bounded in modulus by $1$. Multiplication by the Green function defines unitary operators acting between those spaces. Function $w$ can be recovered from these operators as the characteristic function. It is shown that for Nevanlinna-Pick problem this family of unitary operators extends the family of isometric operators defined by the interpolation data.
Comments15 pages. Submitted to Integral Equations and Operator Theory
