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Let x0,x1, ⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xm ≠ xj, for m ≠ j) and let ym,k, for m = 0, 1, ⋯ , n, and k = 0, 1, ⋯ , rm, with rm ∈ IN, be given real numbers. It is known that there exists a unique polynomial pN− 1 of degree N − 1 with N = ∑ m = 0 n ( r m + 1 ) $N={\sum }_{m = 0}^{n}(r_{m}+ 1)$ , such that p N − 1 ( k ) ( x m ) = y m , k...
In the past few years, Bogoya, Böttcher, Grudsky, and Maximenko obtained the precise asymptotic expansion for the eigenvalues of a Toeplitz matrix Tn(f), under suitable assumptions on the generating function f, as the matrix size n goes to infinity. On the basis of several numerical experiments, it was conjectured by Serra-Capizzano that a completely analogous expansion also holds for the eigenvalues...
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