تقرير
Completeness of systems of inner functions
| العنوان: | Completeness of systems of inner functions |
|---|---|
| المؤلفون: | Miheisi, Nazar |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, Mathematics - Complex Variables, 30B60 (Primary), 30J05 (Secondary) |
| الوصف: | For two inner functions $\vartheta,\varphi\in H^\infty$, we give a simple sufficient condition for the system $\vartheta^m,\; \varphi^n$, $m,n\in\mathbb{Z}$, to be complete in the weak-$^*$ topology of $L^\infty(\mathbb{T})$. To be precise, we show that this system is complete whenever there is an arc $I$ of the unit circle $\mathbb{T}$ such that $\vartheta$ is univalent on $I$ and $\varphi$ is univalent on $\mathbb{T}\setminus I$. As an application of this result, we describe a class of analytic curves $\Gamma$ such that $(\Gamma, \mathcal{X})$ is a Heisenberg uniqueness pair, where $\mathcal{X}$ is the lattice cross $\{(m,n)\in\mathbb{Z}^2:\, mn=0\}$. Our main result extends a theorem of Hedenmalm and Montes-Rodr\'iguez for atomic inner functions with one singularity. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.03076 |
| رقم الأكسشن: | edsarx.2404.03076 |
| قاعدة البيانات: | arXiv |
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