Extending Theorems of Boros and Menzer
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910075938930688 |
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| author | Balcerzak, Marek Popławski, Michał |
| author_facet | Balcerzak, Marek Popławski, Michał |
| contents | We extend results of Boros and Menzer on the alternative equation $f(x)f(y)=0$ for generalized polynomials $f$, and their theorems on the conditional inequality $f(x)f(y)\ge 0$ for generalized monomials $f$ of even degree. We use similar methods and ideas. We replace the largeness, of the respective Borel plane set $D$, in the measure or in the Baire category sense, by its largeness in the mixed measure-category sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25609 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extending Theorems of Boros and Menzer Balcerzak, Marek Popławski, Michał Classical Analysis and ODEs 39B52, 39B55, 39B72 We extend results of Boros and Menzer on the alternative equation $f(x)f(y)=0$ for generalized polynomials $f$, and their theorems on the conditional inequality $f(x)f(y)\ge 0$ for generalized monomials $f$ of even degree. We use similar methods and ideas. We replace the largeness, of the respective Borel plane set $D$, in the measure or in the Baire category sense, by its largeness in the mixed measure-category sense. |
| title | Extending Theorems of Boros and Menzer |
| topic | Classical Analysis and ODEs 39B52, 39B55, 39B72 |
| url | https://arxiv.org/abs/2603.25609 |