Transactions of the American Mathematical Society the Index of Determinacy for Measures and the ¿2-norm of Orthonormal Polynomials
Transactions of the American Mathematical Society the Index of Determinacy for Measures and the ¿2-norm of Orthonormal Polynomials
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美国数学会汇刊测量确定性指数和 ¿
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通讯作者：
A. J. Durán
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作者：
C. Berg;A. J. Durán
对于具有各阶矩的确定性测度，定义并研究了一个确定性指标，它检验了在乘上下列项的偶数次幂时确定性的稳定性 - z是复数。使用该确定性指数，我们解决了确定对于哪个z ∈ C序列（pTz））n（m ∈ N）属于I2的问题，其中（p“）“是与测度ft相关联的正交多项式的序列。
For determinate measures ß having moments of every order we define and study an index of determinacy which checks the stability of determi-nacy under multiplication by even powers of — z for z a complex number. Using this index of determinacy, we solve the problem of determining for which z£C the sequence {pTz))n (m 6 N) belongs to I2 , where (p ") " is the sequence of orthonormal polynomials associated with the measure ft.