On the essential decreasing of the summation order in the Abel-Lidskii sense
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913751911890944 |
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| author | Kukushkin, Maksim V. |
| author_facet | Kukushkin, Maksim V. |
| contents | In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main result, we will show that the summation order can be decreased from the values more than a convergence exponent, in accordance with the Lidskii V.B. result, to an arbitrary small positive number. Additionally, we construct a qualitative theory of summation in the Abel-Lidkii sense and produce a number of fundamental propositions representing the interest themselves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13547 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the essential decreasing of the summation order in the Abel-Lidskii sense Kukushkin, Maksim V. Functional Analysis 47B28, 46B15, 47A10, 47B12, 47B10, 58D25 In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main result, we will show that the summation order can be decreased from the values more than a convergence exponent, in accordance with the Lidskii V.B. result, to an arbitrary small positive number. Additionally, we construct a qualitative theory of summation in the Abel-Lidkii sense and produce a number of fundamental propositions representing the interest themselves. |
| title | On the essential decreasing of the summation order in the Abel-Lidskii sense |
| topic | Functional Analysis 47B28, 46B15, 47A10, 47B12, 47B10, 58D25 |
| url | https://arxiv.org/abs/2306.13547 |