Wiener type theorems for countable limits of quasi-Beurling algebras and maximizing results on weights
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908848533536768 |
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| author | Dabhi, Prakash A. Solanki, Karishman B. |
| author_facet | Dabhi, Prakash A. Solanki, Karishman B. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19557 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wiener type theorems for countable limits of quasi-Beurling algebras and maximizing results on weights Dabhi, Prakash A. Solanki, Karishman B. Functional Analysis Spectral Theory 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. |
| title | Wiener type theorems for countable limits of quasi-Beurling algebras and maximizing results on weights |
| topic | Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2602.19557 |