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Suppose that \(\nu \) is a given positive measure on \(\left [ -1,1\right ] \) . Let \(\mathcal {M}(I,\Lambda )\) denote the set of all measures \(\mu \) , whose restriction to \(\left ( -1,1\right ) \) is \(\nu \) , whose support is contained in a compact interval I, and whose total mass outside \(\left ( -1,1\right ) \) is at most \(\Lambda >0\) . We analyze the measure(s) in \(\mathcal {M}(I,\Lambda )\) whose orthonormal polynomials have largest absolute value among those in \( \mathcal {M}(I,\Lambda )\) at given points.

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Variational Conditions on Extremal Orthonormal Polynomials for Restricted Measures

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  • 发表日期：

    2026年

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  • Doron S. Lubinsky

摘要

Suppose that \(\nu \) is a given positive measure on \(\left [ -1,1\right ] \) . Let \(\mathcal {M}(I,\Lambda )\) denote the set of all measures \(\mu \) , whose restriction to \(\left ( -1,1\right ) \) is \(\nu \) , whose support is contained in a compact interval I, and whose total mass outside \(\left ( -1,1\right ) \) is at most \(\Lambda >0\) . We analyze the measure(s) in \(\mathcal {M}(I,\Lambda )\) whose orthonormal polynomials have largest absolute value among those in \( \mathcal {M}(I,\Lambda )\) at given points.