Schoenberg’s Theorem and Unitarily Invariant Random Arrays

Olav Kallenberg

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Schoenberg’s Theorem and Unitarily Invariant Random Arrays

机译：勋伯格定理和Unit不变随机数组

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Motivated by Schoenberg’s theorem in classical analysis and some recent work on the circular law, we extend the basic representations of unitarily invariant random arrays and functionals to the complex case. As in the real case, the basic building blocks are multiple Wiener–Itô integrals on tensor products of a separable Hilbert space. The complex setting leads to some unexpected simplifications.

机译：受经典的分析中Schoenberg定理的启发以及关于循环法则的一些最新研究的启发，我们将unit不变随机数组和函数的基本表示形式扩展到了复杂的情况。与实际情况一样，基本构件是在可分离的希尔伯特空间的张量积上的多个Wiener–Itô积分。复杂的设置导致一些意想不到的简化。

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《Journal of Theoretical Probability》 |2012年第4期|p.1013-1039|共27页
作者
Olav Kallenberg;
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作者单位

Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL, 36849, USA;

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正文语种 eng
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Random arrays and functionals; Unitary invariance; Gaussian processes; Complex multiple Wiener–Itô integrals; Schoenberg’s theorem; 60B20; 60G09; 28C10; 46G10;

机译：随机数组和泛函;Unit不变性;高斯过程;复杂的多个Wiener-Itô积分;Schoenberg定理;60B20;60G09;28C10;46G10;

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4. Finding Loop Invariants for Programs over Arrays Using a Theorem Prover [C] . Kovacs Laura, Voronkov Andrei 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2009) . 2009

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6. Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables [O] . Tapas K. Chandra, Deli Li, Andrew Rosalsky -1

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8. Unitarily Invariant Generalized Matrix Norms and Hadamard Products [R] . Marcus, M., Kidman, K., Sandy, M. 1984

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Schoenberg’s Theorem and Unitarily Invariant Random Arrays

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