Trigonometric Moment Problem
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High Quality Content by WIKIPEDIA articles! In mathematics, the trigonometric moment problem is formulated as follows: given a finite sequence { 0, ... n }, does there exist a positive Borel measure on the interval [0, 2 ] such that alpha_k = frac{1}{2 pi}int_0 ^{2 pi} e^{-ikt},d mu(t). In other words, an affirmative answer to the problems means that { 0, ... n } are the first n + 1 Fourier coefficients of some positive Borel measure on [0, 2 ].

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High Quality Content by WIKIPEDIA articles! In mathematics, the trigonometric moment problem is formulated as follows: given a finite sequence { 0, ... n }, does there exist a positive Borel measure on the interval [0, 2 ] such that alpha_k = frac{1}{2 pi}int_0 ^{2 pi} e^{-ikt},d mu(t). In other words, an affirmative answer to the problems means that { 0, ... n } are the first n + 1 Fourier coefficients of some positive Borel measure on [0, 2 ].