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Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Alpay, Daniel Colombo, Fabrizio Sabadini, Irene |
| Copyright Year | 2012 |
| Abstract | We study reproducing kernel Hilbert and Pontryagin spaces of slice hyperholomorphic functions. These are analogs of the Hilbert spaces of analytic functions introduced by de Branges and Rovnyak. In the first part of the paper, we focus on the case of Hilbert spaces and introduce, in particular, a version of the Hardy space. Then we define Blaschke factors and Blaschke products and consider an interpolation problem. In the second part of the paper, we turn to the case of Pontryagin spaces. We first prove some results from the theory of Pontryagin spaces in the quaternionic setting and, in particular, a theorem of Shmulyan on densely defined contractive linear relations. We then study realizations of generalized Schur functions and of generalized Carathéodory functions. |
| Starting Page | 87 |
| Ending Page | 125 |
| Page Count | 39 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s11854-013-0028-8 |
| Volume Number | 121 |
| Alternate Webpage(s) | https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1432&context=scs_articles |
| Alternate Webpage(s) | https://arxiv.org/pdf/1203.0234v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s11854-013-0028-8 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
