Central Limit Theorem on Chebyshev Polynomials
نویسنده
چکیده
Let Tl be a transformation on the interval [−1, 1] defined by Chebyshev polynomial of degree l (l ≥ 2), i.e., Tl(cos θ) = cos(lθ). In this paper, we consider Tl as a measure preserving transformation on [−1, 1] with an invariant measure 1 π √ 1−x2 dx. We show that If f(x) is a nonconstant step function with finite kdiscontinuity points with k < l − 1, then it satisfies the Central Limit Theorem. We also give an explicit method how to check whether it satisfies the Central Limit Theorem or not in the cases of general step functions with finite discontinuity points.
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