Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions
By Daniel Alpay, Fabrizio Colombo, Irene Sabadini. Journal d'Analyse Mathematique, 2012
80 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/512f9ac29b0986187f0bdc4c9ba915dc99f913cb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Irene Sabadini
- Fabrizio Colombo
- Daniele C. Struppa
- Daniel Alpay
- Caterina Stoppato
- Graziano Gentili
- M. E. Luna-Elizarrar'as
- M. Shapiro
Citations in the corpus
- A New Resolvent Equation for the $$S$$S-Functional Calculus (2013, unknown): “The reader is referred to [2, 3, 4] for Schur analysis in the slice hyperholomorphic setting and to [1] and [7] for an overview of Schur analysis in the complex setting.”
- Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis (2013, methodology): “the case of Riemann compact surfaces, where the Riemann sphere is replaced by a compact Riemann surface (see [38, 39]), and the more recent developments of Schur analysis in the setting of slice hyperholomorphic functions [40, 41].”
- Entire slice regular functions (2015, background): “The Blaschke products (in the ball case) has been treated in several articles but appeared for the first time in [16].”
- The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum (2014, unknown): “We point out that the S-resolvent operators are also used in Schur analysis in the realization of Schur functions in the slice hyperholomorphic setting see [1, 8, 9, 10] and [3, 11] for the classical case.”