Number of real roots of a random trigonometric polynomial

[摘要] We study the expected number of real roots of the random equationg1cosθ+g2cos2θ+…+gncosnθ=Kwhere the coefficientsgj's are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means ofgj,(j=1,2,…,n), it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.

[学科分类] 应用数学