On Asymptotically Orthonormal Sequences
Emmanuel Fricain, Rishika Rupam
TL;DR
This paper investigates sequences that are nearly orthonormal in specific functional spaces, focusing on their properties and conditions within model and de Branges-Rovnyak spaces.
Contribution
It introduces and analyzes asymptotically orthonormal sequences formed by normalized reproducing kernels in these specialized spaces.
Findings
Characterization of asymptotically orthonormal sequences in model spaces
Conditions for sequences to be nearly orthonormal in de Branges-Rovnyak spaces
Insights into the structure and behavior of such sequences
Abstract
An asymptotically orthonormal sequence is a sequence which is 'nearly' orthonormal in the sense that it satisfies the Parseval equality up to two constants close to one. In this paper, we explore such sequences formed by normalized reproducing kernels of model spaces and de Branges Rovnyak spaces.
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