Abstract
This chapter is concerned with the trigonometric moment problem: Let \(s = (s_{j})_{j\in \mathbb{N}_{0}}\) be a complex sequence. When does there exist a Radon measure μ on the unit circle \(\mathbb{T}\) such that for all \(j \in \mathbb{N}_{0}\), \(s_{j} =\int _{\mathbb{T}}z^{-j}d\mu (z)?\) The truncated trigonometric moment problem is the corresponding problem for a finite sequence (s j ) j = 0 n of prescribed moments.
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Schmüdgen, K. (2017). The Moment Problem on the Unit Circle. In: The Moment Problem. Graduate Texts in Mathematics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-319-64546-9_11
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