Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent
Our first aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten–von Neumann class of the convergence exponent. Considering strictly...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/13/2237 |
| _version_ | 1797434104748179456 |
|---|---|
| author | Maksim V. Kukushkin |
| author_facet | Maksim V. Kukushkin |
| author_sort | Maksim V. Kukushkin |
| collection | DOAJ |
| description | Our first aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten–von Neumann class of the convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms of the norm, we construct a sequence of contours of the power type that contrasts the results by Lidskii, where a sequence of contours of the exponential type was used. |
| first_indexed | 2024-03-09T10:27:29Z |
| format | Article |
| id | doaj.art-b5c865475b9b4c659a71908703b33b8e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:27:29Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b5c865475b9b4c659a71908703b33b8e2023-12-01T21:35:14ZengMDPI AGMathematics2227-73902022-06-011013223710.3390/math10132237Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence ExponentMaksim V. Kukushkin0Moscow State University of Civil Engineering, 129337 Moscow, RussiaOur first aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten–von Neumann class of the convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms of the norm, we construct a sequence of contours of the power type that contrasts the results by Lidskii, where a sequence of contours of the exponential type was used.https://www.mdpi.com/2227-7390/10/13/2237strictly accretive operatorAbel–Lidskii basis propertySchatten–von Neumann classconvergence exponentcounting function |
| spellingShingle | Maksim V. Kukushkin Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent Mathematics strictly accretive operator Abel–Lidskii basis property Schatten–von Neumann class convergence exponent counting function |
| title | Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent |
| title_full | Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent |
| title_fullStr | Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent |
| title_full_unstemmed | Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent |
| title_short | Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent |
| title_sort | natural lacunae method and schatten von neumann classes of the convergence exponent |
| topic | strictly accretive operator Abel–Lidskii basis property Schatten–von Neumann class convergence exponent counting function |
| url | https://www.mdpi.com/2227-7390/10/13/2237 |
| work_keys_str_mv | AT maksimvkukushkin naturallacunaemethodandschattenvonneumannclassesoftheconvergenceexponent |