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Abstract:

Multiplicatively invariant (MI) spaces are closed subspaces of L2(ω, H) that are invariant under multiplication by (some) functions in L∞(ω); they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of functions constructed by taking linear combinations of the generators of a finitely generated MI space is a new set of generators for the same space, and we give necessary and sufficient conditions on the linear combinations to preserve frame properties. We then apply our results on MI spaces to systems of translates in the context of locally compact abelian groups and we extend some results previously proven for systems of integer translates in L2(ℝd). © Instytut Matematyczny PAN, 2015.

Registro:

Documento: Artículo
Título:Linear combinations of generators in multiplicatively invariant spaces
Autor:Paternostro, V.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Buenos Aires, 1428, Argentina
IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Palabras clave:Fibers; Frame; Gramian; LCA groups; Multiplicatively invariant spaces; Range functions; Shift invariant space
Año:2015
Volumen:226
Número:1
Página de inicio:1
Página de fin:16
DOI: http://dx.doi.org/10.4064/sm226-1-1
Título revista:Studia Mathematica
Título revista abreviado:Stud. Math.
ISSN:00393223
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v226_n1_p1_Paternostro

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Citas:

---------- APA ----------
(2015) . Linear combinations of generators in multiplicatively invariant spaces. Studia Mathematica, 226(1), 1-16.
http://dx.doi.org/10.4064/sm226-1-1
---------- CHICAGO ----------
Paternostro, V. "Linear combinations of generators in multiplicatively invariant spaces" . Studia Mathematica 226, no. 1 (2015) : 1-16.
http://dx.doi.org/10.4064/sm226-1-1
---------- MLA ----------
Paternostro, V. "Linear combinations of generators in multiplicatively invariant spaces" . Studia Mathematica, vol. 226, no. 1, 2015, pp. 1-16.
http://dx.doi.org/10.4064/sm226-1-1
---------- VANCOUVER ----------
Paternostro, V. Linear combinations of generators in multiplicatively invariant spaces. Stud. Math. 2015;226(1):1-16.
http://dx.doi.org/10.4064/sm226-1-1