Complex Zeros of Trigonometric Polynomials with Standard Normal Random Coefficients

In this paper, we obtain an exact formula for the average density of the distribution of complex zeros of a random trigonometric polynomial η0+η1cosθ+η2cos2θ+⋯+ηncosnθ in (0,2π), where the coefficients ηj=aj+ιbj, and {aj}j=1n and {bj}j=1n are sequences of independent normally distributed random vari...

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Vydané v:	Journal of mathematical analysis and applications Ročník 262; číslo 2; s. 554 - 563
Hlavní autori:	Farahmand, K., Grigorash, A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	San Diego, CA Elsevier Inc 15.10.2001 Elsevier
Predmet:	Adler's theorem complex roots coordinate transform density of zeros Exact sciences and technology Jacobian of transformation Mathematical analysis Mathematics Number of complex zeros random algebraic polynomials random trigonometric polynomials real roots Sciences and techniques of general use Special functions Adler's theorem real roots random trigonometric polynomials coordinate transform complex roots random algebraic polynomials Jacobian of transformation density of zeros Number of complex zeros Zero of function Random polynomial Coodinate transformation Adler theorem Trigonometric polynomial Special function Jacobi matrix Algebraic polynomial Complex number
ISSN:	0022-247X, 1096-0813
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