Model subspaces techniques to study Fourier expansions in L2 spaces associated to singular measures

Let μ be a probability measure on T that is singular with respect to the Haar measure. In this paper we study Fourier expansions in L² (T, μ) using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials {zⁿ} n ∈ N is effective in L² (T, μ) , it has a Parsev...

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Autores principales: Antezana, Jorge Abel, García, María Guadalupe
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2020
Materias:
Matemática
Model subspaces
Kaczmarz algorithm
Fourier expansions
Parseval frames
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/128403
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-128403
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Model subspaces
Kaczmarz algorithm
Fourier expansions
Parseval frames
spellingShingle Matemática
Model subspaces
Kaczmarz algorithm
Fourier expansions
Parseval frames
Antezana, Jorge Abel
García, María Guadalupe
Model subspaces techniques to study Fourier expansions in L2 spaces associated to singular measures
topic_facet Matemática
Model subspaces
Kaczmarz algorithm
Fourier expansions
Parseval frames
description Let μ be a probability measure on T that is singular with respect to the Haar measure. In this paper we study Fourier expansions in L² (T, μ) using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials {zⁿ} n ∈ N is effective in L² (T, μ) , it has a Parseval frame associated via the Kaczmarz algorithm. Our first main goal is to identify the aforementioned frame with boundary values of the frame P φ (zⁿ) for the model subspace H (φ) = H² ⊖ φ H² , where P φ is the orthogonal projection from the Hardy space H² onto H (φ). The study of Fourier expansions in L² (T,μ) also leads to consider positive kernels in the Hardy space. Our second main goal is to study the set of measures μ which reproduce a kernel contained in a model subspace. We completely characterize this set when the kernel is the reproducing kernel of a model subspace, and we study the consequences of this characterization.
format Articulo
Preprint
author Antezana, Jorge Abel
García, María Guadalupe
author_facet Antezana, Jorge Abel
García, María Guadalupe
author_sort Antezana, Jorge Abel
title Model subspaces techniques to study Fourier expansions in L2 spaces associated to singular measures
title_short Model subspaces techniques to study Fourier expansions in L2 spaces associated to singular measures
title_full Model subspaces techniques to study Fourier expansions in L2 spaces associated to singular measures
title_fullStr Model subspaces techniques to study Fourier expansions in L2 spaces associated to singular measures
title_full_unstemmed Model subspaces techniques to study Fourier expansions in L2 spaces associated to singular measures
title_sort model subspaces techniques to study fourier expansions in l2 spaces associated to singular measures
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/128403
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AT garciamariaguadalupe modelsubspacestechniquestostudyfourierexpansionsinl2spacesassociatedtosingularmeasures
bdutipo_str Repositorios
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