تقرير
A Fermionic Grunsky operator
| العنوان: | A Fermionic Grunsky operator |
|---|---|
| المؤلفون: | Kristel, Peter, Schippers, Eric, Staubach, Wolfgang |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, Mathematical Physics, Mathematics - Differential Geometry, Mathematics - Functional Analysis, Mathematics - Representation Theory |
| الوصف: | To a conformal map $f$ from the disk $\mathbb{D}$ into the complex plane onto a domain with rectifiable Ahlfors-regular boundary, we associate a new kind of Grunsky operator on the Hardy space of the unit disk. This is analogous to the classical Grunsky operator, which itself can be viewed as an operator on Bergman or Dirichlet space. We show that the pull-back of the Smirnov space of the complement of $f(\mathbb{D})$ by $f$ is the graph of the Grunsky operator. We also characterize those domains with rectifiable Ahlfors-regular boundaries such that the Grunsky operator is Hilbert-Schmidt. In particular, we show that if the Grunsky operator is Hilbert-Schmidt, then $f(\mathbb{D})$ is a Weil-Petersson quasidisk. The formulations of the results and proofs make essential use of a geometric treatment of Smirnov space as a space of half-order differentials. |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2311.12972Test |
| رقم الانضمام: | edsarx.2311.12972 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |