The spectral analysis of the difference quotient operator on model spaces
We conduct a spectral analysis of the difference quotient operator Q ζ u , associated with a boundary point ζ ∈ ∂ D , on the model space K u . We describe the operator's spectrum and provide both upper and lower estimates for its norm ‖ Q ζ u ‖ , and furthermore discussing the sharpness of these bounds. Notably, the upper estimate offers a new characterization of the one-component property for inner functions.
Authors
- Javad Mashreghi (ORCID: https://orcid.org/0000-0002-7969-9576)
- Carlo Bellavita (ORCID: https://orcid.org/0000-0003-3136-0271)
- Eugenio Dellepiane (ORCID: https://orcid.org/0009-0005-3432-2053)
Institutions
- Politecnico di Torino (IT)
- Laboratoire de Mathématiques d'Orsay (FR)
- Université Laval (CA)
- Universitat de Barcelona (ES)
Publication Details
- Journal
- Bulletin des Sciences Mathématiques
- Published
- 2025-05-29
- DOI
- https://doi.org/10.1016/j.bulsci.2025.103673
- Citations
- 1
- Primary Topic
- Holomorphic and Operator Theory
- Type
- article
- Field-Weighted Citation Impact
- 3.73
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Canada Research Chairs
- Ministerio de Ciencia e Innovación
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- Natural Sciences and Engineering Research Council of Canada