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arXiv · 2602.19557

Wiener type theorems for countable limits of quasi-Beurling algebras and maximizing results on weights

Prakash A. Dabhi·Karishman B. Solanki
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Abstract

We establish the vector-valued Wiener type theorems for countable projective and inductive limits of quasi-Banach algebras in a weighted setting for both finite and infinite dimensional cases. As an application, we extend the notions of rapidly decreasing and exponentially decreasing sequence spaces using quasi-Beurling algebras and show that they are inverse-closed; and obtain a hierarchy of inverse-closed vector-valued algebras using weights. In addition, we derive maximizing results on weights for the nonadmissible weighted version of Wiener's theorem in both discrete and continuous cases.

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Prakash A. Dabhi, Karishman B. Solanki. 2026-02-23. Wiener type theorems for countable limits of quasi-Beurling algebras and maximizing results on weights. https://arxiv.org/abs/2602.19557

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