تقرير
Spectra of infinitesimal generators of composition semigroups on weighted Bergman spaces induced by doubling weights
| العنوان: | Spectra of infinitesimal generators of composition semigroups on weighted Bergman spaces induced by doubling weights |
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| المؤلفون: | Qian, Ruishen, Wu, Fanglei, Wulan, Hasi |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, Mathematics - Complex Variables |
| الوصف: | Suppose $(C_t)_{t\geq0}$ is the composition semigroup induced by a one-parameter semigroup $(\varphi_t)_{t\geq0}$ of analytic self-maps of the unit disk. The main purpose of the paper is to investigate the spectrum of the infinitesimal generator of $(C_t)_{t\geq0}$ acting on the weighted Bergman space induced by doubling weights, provided $(\varphi_t)_{t\geq0}$ is elliptic. The method applied is a certain spectral mapping theorem and a characterization of the spectra of certain composition operators. Eventual norm-continuity of $(C_t)_{t\geq0}$ also plays an important role, which can be depicted in terms of studying the difference of two distinct composition operators. As a byproduct, we also characterize a certain compact integral operator that is closely related to the resolvent of the infinitesimal generator of $(C_t)_{t\geq0}$. Comment: The first version. Every comments are welcomed |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.13662 |
| رقم الأكسشن: | edsarx.2405.13662 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |