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Moment problems and bounds for matrix-valued smeared spectral functions
Ryan Abbott, William I. Jay, Patrick R. Oare
https://arxiv.org/abs/2508.01377 https://

Moment problems and bounds for matrix-valued smeared spectral functions
Numerical analytic continuation arises frequently in lattice field theory, particularly in spectroscopy problems. This work shows the equivalence of common spectroscopic problems to certain classes of moment problems that have been studied thoroughly in the mathematical literature. Mathematical results due to Kovalishina enable rigorous bounds on smeared matrix-valued spectral functions, which are implemented numerically for the first time. The required input is a positive-definite matrix of Eu…