Summable analogous to the Ivashev-Musatov Theorems

Adem Limani

doi:10.48550/arxiv.2505.08980

May 13, 2025Open Access

Summable analogous to the Ivashev-Musatov Theorems

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Key Points

The study introduces summable analogues of the Ivashev-Musatov Theorem, uncovering unique properties.
Found elements with pathological support and range in weighted $l^1$ and Orlicz spaces indicate new thresholds.
Results build on and complement foundational works by J. P. Kahane, Y. Katznelson, and T. W. K"orner.
Insights from the analysis may influence further research in topology and measure theory.

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Abstract

We investigate summable analogues of the classical Ivashev-Musatov Theorem and threshold phenomenons alike. In the setting of weighted ¹ and Orlicz sequence spaces, we exhibit elements with critically pathological support and range, both topologically and in the sense of measure theory. Our results complement earlier works of J. P. Kahane, Y. Katznelson and T. W. K\"orner.

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Adem Limani (2025) studied this question.

synapsesocial.com/papers/68e82b12e7fc21a3005002a8 https://doi.org/10.48550/arxiv.2505.08980

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Summable analogous to the Ivashev-Musatov Theorems

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Summable analogous to the Ivashev-Musatov Theorems

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