函数演算生成的框架
Frames from Functional Calculus
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中文总结 AI 辅助
研究通过函数演算将函数族应用于对角算子生成框架的问题，对于特定谱证明分数阶算子幂系统在满足角限制时是框架，给出更一般连续函数生成框架的\(\ell^2\)扰动准则，拓宽了动态采样等问题中结构化框架类别。
中文摘要 AI 辅助
我们通过函数演算将函数族应用于对角算子来生成框架，其对角元素构成卡尔松插值序列。首先，对于包含在斯托尔兹域和角扇形中的分离谱，我们证明当步长满足自然角限制时，分数阶算子幂系统仍是框架，这扩展了正实谱的早期结果并允许非整数幂，且角限制通常是尖锐的。其次，在包含谱的曲线上假设密度条件，我们给出了由更一般连续函数生成的框架的\(\ell^2\)扰动准则。这些结果拓宽了动态采样及相关算子轨道问题中可用的结构化框架类别。
英文摘要
We introduce frames generated by applying families of functions to a diagonal operator through functional calculus, with diagonal entries forming a Carleson interpolating sequence. First, for separated spectra contained in a Stolz domain and an angular sector, we prove that systems of fractional operator powers remain frames whenever the step size satisfies the natural angular restriction. This extends earlier results for positive real spectra and permits noninteger powers. We also show that the angular restriction is sharp in general. Second, we give an $\ell^2$-perturbation criterion for frames generated by more general continuous functions, assuming a density condition on a curve containing the spectrum. The results broaden the class of structured frames available in dynamical sampling and related operator-orbit problems.
