On Asymptotically Orthonormal
Sequences

Fricain, Emmanuel; Rupam, Rishika

doi:10.4153/cjm-2017-001-9

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Introduction and Main Results1

Families Of Reproducing Kernels and Their Projections1

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2023

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Cited by 3 publications

(2 citation statements)

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“…Families whose Gram matrices have such a form are asymptotically orthonormal families (see the definition in Section 2 below) and are widely studied (see, for example, [4,8,7,9,10,6]).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Schur-Nevanlinna parameters, Riesz bases, and compact Hankel operators on the model space

Boricheva¹

2022

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We study Riesz bases/Riesz sequences of reproducing kernels in the model space K θ in connection with the corresponding Schur-Nevanlinna parameters and functions. In particular, we construct inner functions with given Schur-Nevanlinna parameters at a given sequence Λ such that the corresponding systems of projections of reproducing kernels in the model space are complete/non complete. Furthermore, we give a compactness criterion for Hankel operators with symbol θB, where θ is an inner function and B is an interpolating Blaschke product and use this criterion to describe Riesz bases K Λ,θ , with lim λ∈Λ,|λ|→1 θ(λ) = 0.

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“…Families whose Gram matrices have such a form are asymptotically orthonormal families (see the definition in Section 2 below) and are widely studied (see, for example, [4,8,7,9,10,6]).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Theorem on U +S ∞ families. (see [6,7]) Let X be a family of vectors {x n } n≥1 in a Hilbert space. We denote by G(X) the Gram matrix of X.…”

Section: Families Of Reproducing Kernels and Their Projectionsmentioning

confidence: 99%

Schur-Nevanlinna parameters, Riesz bases, and compact Hankel operators on the model space

Boricheva¹

2022

Preprint

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Asymptotically orthonormal basis and Toeplitz operators

Fricain

Rupam

2019

Journal of Mathematical Analysis and Applications

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Recently, M. Mitkovski [Mit17] gave a criterion for the basicity of a sequence of complex exponentials in terms of the invertibility properties of a certain naturally associated Toeplitz operator, in the spirit of the celebrated work of Khrushchëv-Nikolski-Pavlov [HNP81]. In our paper, we extend the results of Mitkovski to model spaces associated with meromorphic inner functions and we also give an analogue for the property of being an asymptotically orthonormal basis.2010 Mathematics Subject Classification. 30J05, 30H10.

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Schur–Nevanlinna parameters, Riesz bases, and compact Hankel operators on the model space

Boricheva

2023

Journal of Mathematical Analysis and Applications

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On Asymptotically Orthonormal Sequences

Cited by 3 publications

References 9 publications

Schur-Nevanlinna parameters, Riesz bases, and compact Hankel operators on the model space

Schur-Nevanlinna parameters, Riesz bases, and compact Hankel operators on the model space

Asymptotically orthonormal basis and Toeplitz operators

Schur–Nevanlinna parameters, Riesz bases, and compact Hankel operators on the model space

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