φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS

다국어 초록 (Multilingual Abstract)

We introduce φ-frames in L^2(G), as a generalization of a-frames dened in [8], where G is a locally compact Abelian group and φ is a topological automorphism on G. We give a characterization of φ-frames with regard to usual frames in L^2(G) and show that φ-frames share several useful properties with frames. We dene the associated φ-analysis and φ-preframe operators, with which we obtain criteria for a sequence to be a φ-frame or a φ-Bessel sequence. We also define φ-Riesz bases in L^2(G) and establish equivalent conditions for a sequence in L^2(G) to be a φ-Riesz basis.

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