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A solution of the trigonometric moment problem via Tagamlitzki’s ”Theorem of the cones”. (English) Zbl 0735.42007

A sequence \(\{c_ n\}_{n=-\infty}^ \infty\) of complex numbers is a moment sequence if there exists a nondecreasing function \(\alpha:[0,2\pi]\to\mathbb{R}\) such that the inequalities \[ c_ n=\int_ 0^{2\pi}e^{int}d\alpha(t),\qquad n\in\mathbb{Z}, \] hold. Using Tagamlitzki’s “Theorem of the cones”, the author proves a classical F. Riesz’ theorem about trigonometric moment problem.

MSC:

42A70 Trigonometric moment problems in one variable harmonic analysis
30E05 Moment problems and interpolation problems in the complex plane
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