Modern spectral estimation techniques often rely on second order statistics of a time-series to determine a power spectrum consistent with data. Such statistics provide moment constraints on the power spectrum. In this paper we study possible distance functions between spectra which permit a reasonable quantitative description of the uncertainty in moment problems. Typically, there is an infini...

Abstract In Kiukas, Lahti, and Ylinen (2006, Journal of Mathematical Physics 47, 072104), the authors asked following general question. When is a positive operator measure projection valued? A version this question formulated in terms moments was posed Pietrzycki Stochel (2021, Functional Analysis 280, 109001). Let T be self-adjoint operator, let F Borel semispectral on real line with compact s...