Linear combinations of generators in multiplicatively invariant spaces

• Autorzy: Victoria Paternostro
• Języki publikacji: EN

Abstrakty

EN

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 $L²(ℝ^{d})$.

Kategorie tematyczne

• 42C40: Wavelets and other special systems
• 42C15: General harmonic expansions, frames
• 43A70: Analysis on specific locally compact and other abelian groups
• 22B99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 226
• Numer: 1
• Strony: 1-16

Daty

wydano

2015

Twórcy

autor

Victoria Paternostro

• Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
• IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina

Identyfikatory

DOI

10.4064/sm226-1-1