Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series
A criterion for boundedness of composition operators acting on a class of Hilbert spaces of entire Dirichlet series, namely the class ℋ(E, β ) , was obtained in Hou et al. (J. Math. Anal. Appl. 401: 416–429, 2013) for those spaces that do not contain non-zero constant functions, while other possibil...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/150284 |
| _version_ | 1811683987513409536 |
|---|---|
| author | Doan, Minh Luan Mau, Camille Khoi, Le Hai |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Doan, Minh Luan Mau, Camille Khoi, Le Hai |
| author_sort | Doan, Minh Luan |
| collection | NTU |
| description | A criterion for boundedness of composition operators acting on a class of Hilbert spaces of entire Dirichlet series, namely the class ℋ(E, β ) , was obtained in Hou et al. (J. Math. Anal. Appl. 401: 416–429, 2013) for those spaces that do not contain non-zero constant functions, while other possibilities were not studied. In this paper, we first provide a complete characterization of boundedness of composition operators on any space ℋ(E, β ) , which may or may not contain constant functions. We then study complex symmetry of composition operators on ℋ(E, β ) , via analysis of composition conjugations. |
| first_indexed | 2024-10-01T04:21:28Z |
| format | Journal Article |
| id | ntu-10356/150284 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:21:28Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1502842023-02-28T19:25:47Z Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series Doan, Minh Luan Mau, Camille Khoi, Le Hai School of Physical and Mathematical Sciences Science::Mathematics Hilbert Space Entire Dirichlet Series A criterion for boundedness of composition operators acting on a class of Hilbert spaces of entire Dirichlet series, namely the class ℋ(E, β ) , was obtained in Hou et al. (J. Math. Anal. Appl. 401: 416–429, 2013) for those spaces that do not contain non-zero constant functions, while other possibilities were not studied. In this paper, we first provide a complete characterization of boundedness of composition operators on any space ℋ(E, β ) , which may or may not contain constant functions. We then study complex symmetry of composition operators on ℋ(E, β ) , via analysis of composition conjugations. Ministry of Education (MOE) Nanyang Technological University Accepted version The second-named author was supported in part by the CN Yang Scholars Programme, Nanyang Technological University. The third-named author was supported in part by MOE’s AcRF Tier 1 grant M4011724.110 (RG128/16). 2021-05-20T05:48:49Z 2021-05-20T05:48:49Z 2019 Journal Article Doan, M. L., Mau, C. & Khoi, L. H. (2019). Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series. Vietnam Journal of Mathematics, 47(2), 443-460. https://dx.doi.org/10.1007/s10013-018-00330-6 2305-221X 0000-0002-4282-3449 https://hdl.handle.net/10356/150284 10.1007/s10013-018-00330-6 2-s2.0-85069881359 2 47 443 460 en M4011724.110 (RG128/16) Vietnam Journal of Mathematics © 2019, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. All rights reserved. This paper was published by Springer in Vietnam Journal of Mathematics and is made available with permission of Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. application/pdf |
| spellingShingle | Science::Mathematics Hilbert Space Entire Dirichlet Series Doan, Minh Luan Mau, Camille Khoi, Le Hai Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series |
| title | Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series |
| title_full | Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series |
| title_fullStr | Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series |
| title_full_unstemmed | Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series |
| title_short | Complex symmetry of composition operators on Hilbert spaces of entire Dirichlet series |
| title_sort | complex symmetry of composition operators on hilbert spaces of entire dirichlet series |
| topic | Science::Mathematics Hilbert Space Entire Dirichlet Series |
| url | https://hdl.handle.net/10356/150284 |
| work_keys_str_mv | AT doanminhluan complexsymmetryofcompositionoperatorsonhilbertspacesofentiredirichletseries AT maucamille complexsymmetryofcompositionoperatorsonhilbertspacesofentiredirichletseries AT khoilehai complexsymmetryofcompositionoperatorsonhilbertspacesofentiredirichletseries |