p，q-正弦函数的基性质
Basis properties of the p,q-sine functions
摘要：
我们改进了目前已知的周期扩张p，q-正弦函数族的基性阈值。我们的研究结果依赖于Beurling分解的相应的坐标变化的移位算子的无限重。我们还确定了与这个家庭的Riesz常数的界限。这些结果填补了现有文献中关于这一问题的数学空白。
英文摘要：
We improve the currently known thresholds for basisness of the family of periodically dilated p,q-sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity. We also determine refined bounds on the Riesz constant associated to this family. These results seal mathematical gaps in the existing literature on the subject.
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。
