An Estimate for the Steklov Zeta Function of a Planar Domain Derived from a First Variation Formula Научная публикация
| Журнал |
Journal of Geometric Analysis
ISSN: 1050-6926 , E-ISSN: 1559-002X |
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| Вых. Данные | Год: 2022, Том: 32, Номер: 5, Номер статьи : 161, Страниц : DOI: 10.1007/s12220-022-00890-7 | ||||
| Ключевые слова | Dirichlet-to-Neumann operator; Inverse spectral problem; Steklov spectrum; Zeta function | ||||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Российский фонд фундаментальных исследований | 20-51-15004 |
Реферат:
We consider the Steklov zeta function ζΩ of a smooth bounded simply connected planar domain Ω⊂ R2 of perimeter 2 π. We provide a first variation formula for ζΩ under a smooth deformation of the domain. On the base of the formula, we prove that, for every s∈ (- 1 , 0) ∪ (0 , 1) , the difference ζΩ(s) - 2 ζR(s) is non-negative and is equal to zero if and only if Ω is a round disk (ζR is the classical Riemann zeta function). Our approach gives also an alternative proof of the inequality ζΩ(s) - 2 ζR(s) ≥ 0 for s∈ (- ∞, - 1] ∪ (1 , ∞) ; the latter fact was proved in our previous paper (2018) in a different way. We also provide an alternative proof of the equality ζΩ′(0)=2ζR′(0) obtained by Edward and Wu (Determinant of the Neumann operator on smooth Jordan curves. Proc Am Math Soc 111(2):357–363, 1991).
Библиографическая ссылка:
Jollivet A.
, Sharafutdinov V.
An Estimate for the Steklov Zeta Function of a Planar Domain Derived from a First Variation Formula
Journal of Geometric Analysis. 2022. V.32. N5. 161 . DOI: 10.1007/s12220-022-00890-7 WOS Scopus РИНЦ OpenAlex
An Estimate for the Steklov Zeta Function of a Planar Domain Derived from a First Variation Formula
Journal of Geometric Analysis. 2022. V.32. N5. 161 . DOI: 10.1007/s12220-022-00890-7 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 4 февр. 2022 г. |
| Принята к публикации: | 11 февр. 2022 г. |
| Опубликована online: | 9 мар. 2022 г. |
| Опубликована в печати: | 10 мая 2022 г. |
Идентификаторы БД:
| Web of science: | WOS:000766588900001 |
| Scopus: | 2-s2.0-85126222047 |
| РИНЦ: | 48190144 |
| OpenAlex: | W3014425014 |