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Abstract:

Let H be Hilbert space and (Ω, m) a σ-finite measure space. Multiplicatively invariant (MI) spaces are closed subspaces of L2(Ω, H) that are invariant under point-wise multiplication by functions from a fixed subset of L∞(Ω). Given a finite set of data F ⊆ L2 (Ω, H), in this paper we prove the existence and construct an MI space M that best fits F, in the least squares sense. MI spaces are related to shift-invariant (SI) spaces via a fiberization map, which allows us to solve an approximation problem for SI spaces in the context of locally compact abelian groups. On the other hand, we introduce the notion of decomposable MI spaces (MI spaces that can be decomposed into an orthogonal sum of MI subspaces) and solve the approximation problem for the class of these spaces. Since SI spaces having extra invariance are in one-to-one relation to decomposable MI spaces, we also solve our approximation problem for this class of SI spaces. Finally we prove that translation-invariant spaces are in correspondence with totally decomposable MI spaces. © 2017 American Mathematical Society.

Registro:

Documento: Artículo
Título:An approximation problem in multiplicatively invariant spaces
Autor:Cabrelli, C.; Mosquera, C.A.; Paternostro, V.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Univer-sidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Palabras clave:Approximation; Extra invariance; Multiplicatively invariant spaces; Shift-invariant spaces
Año:2017
Volumen:693
Página de inicio:143
Página de fin:165
DOI: http://dx.doi.org/10.1090/conm/693/13934
Título revista:Contemporary Mathematics
Título revista abreviado:Contemp. Math.
ISSN:02714132
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02714132_v693_n_p143_Cabrelli

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Citas:

---------- APA ----------
Cabrelli, C., Mosquera, C.A. & Paternostro, V. (2017) . An approximation problem in multiplicatively invariant spaces. Contemporary Mathematics, 693, 143-165.
http://dx.doi.org/10.1090/conm/693/13934
---------- CHICAGO ----------
Cabrelli, C., Mosquera, C.A., Paternostro, V. "An approximation problem in multiplicatively invariant spaces" . Contemporary Mathematics 693 (2017) : 143-165.
http://dx.doi.org/10.1090/conm/693/13934
---------- MLA ----------
Cabrelli, C., Mosquera, C.A., Paternostro, V. "An approximation problem in multiplicatively invariant spaces" . Contemporary Mathematics, vol. 693, 2017, pp. 143-165.
http://dx.doi.org/10.1090/conm/693/13934
---------- VANCOUVER ----------
Cabrelli, C., Mosquera, C.A., Paternostro, V. An approximation problem in multiplicatively invariant spaces. Contemp. Math. 2017;693:143-165.
http://dx.doi.org/10.1090/conm/693/13934