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Transactions of the American Mathematical Society

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On the number of real zeros of a random trigonometric polynomial


Author: M. Sambandham
Journal: Trans. Amer. Math. Soc. 238 (1978), 57-70
MSC: Primary 60G17
DOI: https://doi.org/10.1090/S0002-9947-1978-0461648-4
MathSciNet review: 0461648
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Abstract: For the random trigonometric polynomial

$\displaystyle \sum\limits_{n = 1}^N {{g_n}(t)\cos n\theta ,} $

where $ {g_n}(t),0 \leqslant t \leqslant 1$, are dependent normal random variables with mean zero, variance one and joint density function

$\displaystyle \vert M{\vert^{1/2}}{(2\pi )^{ - N/2}}\exp [ - (1/2)\bar a'M\bar a]$

where $ {M^{ - 1}}$ is the moment matrix with $ {\rho _{ij}} = \rho ,0 < \rho < 1,i \ne j,i,j = 1,2, \ldots ,N$ and $ \bar a$ is the column vector, we estimate the probable number of zeros.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0461648-4
Article copyright: © Copyright 1978 American Mathematical Society

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