Sobolev Lifting over Invariants
We prove lifting theorems for complex representations of finite groups . Let σ = (σ₁,…, σₙ) be a minimal system of homogeneous basic invariants and let be their maximal degree. We prove that any continuous map ̅ : ℝᵐ → such that = σ ∘ ̅ is of class ᵈ⁻¹'¹ is locally of Sobolev class ¹'...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2021 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211312 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Sobolev Lifting over Invariants. Adam Parusiński and Armin Rainer. SIGMA 17 (2021), 037, 31 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862628090597867520 |
|---|---|
| author | Parusiński, Adam Rainer, Armin |
| author_facet | Parusiński, Adam Rainer, Armin |
| citation_txt | Sobolev Lifting over Invariants. Adam Parusiński and Armin Rainer. SIGMA 17 (2021), 037, 31 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove lifting theorems for complex representations of finite groups . Let σ = (σ₁,…, σₙ) be a minimal system of homogeneous basic invariants and let be their maximal degree. We prove that any continuous map ̅ : ℝᵐ → such that = σ ∘ ̅ is of class ᵈ⁻¹'¹ is locally of Sobolev class ¹'ᵖ for all 1 ≤ < /(−1). In the case = 1, there always exists a continuous choice ̅ for given f: ℝ →σ() ⊆ ℂⁿ. We give uniform bounds for the ¹'ᵖ-norm of ̅ in terms of the ᵈ⁻¹'¹-norm of . The result is optimal: in general, a lifting ̅ cannot have a higher Sobolev regularity, and it even might not have bounded variation if is in a larger Hölder class.
|
| first_indexed | 2026-03-14T16:44:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211312 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T16:44:01Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Parusiński, Adam Rainer, Armin 2025-12-29T11:08:59Z 2021 Sobolev Lifting over Invariants. Adam Parusiński and Armin Rainer. SIGMA 17 (2021), 037, 31 pages 1815-0659 2020 Mathematics Subject Classification: 22E45;26A16;46E35;14L24 arXiv:2003.01967 https://nasplib.isofts.kiev.ua/handle/123456789/211312 https://doi.org/10.3842/SIGMA.2021.037 We prove lifting theorems for complex representations of finite groups . Let σ = (σ₁,…, σₙ) be a minimal system of homogeneous basic invariants and let be their maximal degree. We prove that any continuous map ̅ : ℝᵐ → such that = σ ∘ ̅ is of class ᵈ⁻¹'¹ is locally of Sobolev class ¹'ᵖ for all 1 ≤ < /(−1). In the case = 1, there always exists a continuous choice ̅ for given f: ℝ →σ() ⊆ ℂⁿ. We give uniform bounds for the ¹'ᵖ-norm of ̅ in terms of the ᵈ⁻¹'¹-norm of . The result is optimal: in general, a lifting ̅ cannot have a higher Sobolev regularity, and it even might not have bounded variation if is in a larger Hölder class. Supported by the Austrian Science Fund (FWF), Grant P 32905-N and START Programme Y963, and by ANR project ANR-17-CE40-0023- LISA. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Sobolev Lifting over Invariants Article published earlier |
| spellingShingle | Sobolev Lifting over Invariants Parusiński, Adam Rainer, Armin |
| title | Sobolev Lifting over Invariants |
| title_full | Sobolev Lifting over Invariants |
| title_fullStr | Sobolev Lifting over Invariants |
| title_full_unstemmed | Sobolev Lifting over Invariants |
| title_short | Sobolev Lifting over Invariants |
| title_sort | sobolev lifting over invariants |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211312 |
| work_keys_str_mv | AT parusinskiadam sobolevliftingoverinvariants AT rainerarmin sobolevliftingoverinvariants |