Two footnotes to the F. & M. Riesz theorem

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New proof reveals an elementary inequality connecting the F. & M. Riesz theorem with Hilbert's criterion in analytic measures.

The new proof clarifies the relationship between the F. & M. Riesz theorem and Hilbert's criterion, enhancing understanding of analytic measures.
The elementary inequality provides a clearer approach to the theorem, indicating new insights in the context of analytic functions on the unit circle.
This proof extends to the infinite-dimensional torus, linking results in different mathematical contexts while maintaining core concepts.
The research highlights the importance of norms in function space, specifically the L^1 norm, in analyzing analytic measures.

Ole Fredrik Brevig (2025) studied this question.

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