AI 中文总结
该研究扩展了Totik的加权正交多项式定理，分析带变权区间上正交多项式的强渐近行为，相关平衡测度支撑集可收敛至真子区间或坍缩为单点，为多重正交应用提供支撑。
AI 中文摘要
我们研究带变权区间上正交多项式的强渐近行为，扩展了Totik关于加权正交多项式的定理框架。结果在多个方向推广了该定理，特别允许相关平衡测度的支撑集收敛到原正交区间的真子区间，甚至坍缩为单点。这些扩展由多重正交中的应用驱动，这类变测度在该场景中自然产生。
英文摘要
We study strong asymptotics of orthogonal polynomials on an interval with varying weights, extending the framework of Totik's theorem on weighted orthogonal polynomials. Our results generalize this theorem in several directions. In particular, we allow the supports of the associated equilibrium measures to converge to a proper subinterval of the original interval of orthogonality or even collapse to a point. These extensions are motivated by applications to multiple orthogonality where such varying measures arise naturally.
