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φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS
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 Title & Authors
φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS
Gol, Rajab Ali Kamyabi; Tousi, Reihaneh Raisi;
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 Abstract
We introduce -frames in (G), as a generalization of a-frames defined in [8], where G is a locally compact Abelian group and is a topological automorphism on G. We give a characterization of -frames with regard to usual frames in (G) and show that -frames share several useful properties with frames. We define the associated -analysis and -preframe operators, with which we obtain criteria for a sequence to be a -frame or a -Bessel sequence. We also define -Riesz bases in (G) and establish equivalent conditions for a sequence in (G) to be a -Riesz basis.
 Keywords
-bracket product;-factorable operator;-frame;-Riesz basis;locally compact Abelian group;
 Language
English
 Cited by
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