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We introduce φ-frames in L^2(G), as a generalization of a-frames de ned 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 de ne 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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참고문헌 (27)
참고문헌 신청
A. Aldroubi / 2001 / p-frames and shift invariant subspaces of Lp / J. Fourier Anal. Appl 7 (1) : 1 ~ 21
A. Ron / 1995 / Frames and stable bases for shift-invariant subspaces of L2(Rd) / Canad. J. Math 47 (5) : 1051 ~ 1094
C. de Boor / 1994 / The structure of nitely generated shift-invariant spaces in L2(Rd) / J. Funct. Anal 119 (1) : 37 ~ 78
E. Hernandez / 1996 / A First Course on Wavelets, Studies in Advanced Mathematics / CRC Press
E. Hewitt / 1963 / Abstract Harmonic Analysis. Vol. I: Structure of topological groups. Integration theory, group representations / Springer-Verlag
A. Ron / 1995 / Frames and stable bases for shift-invariant subspaces of L2(Rd) / Canad. J. Math 47 (5) : 1051 ~ 1094
C. de Boor / 1994 / The structure of nitely generated shift-invariant spaces in L2(Rd) / J. Funct. Anal 119 (1) : 37 ~ 78
E. Hernandez / 1996 / A First Course on Wavelets, Studies in Advanced Mathematics / CRC Press
E. Hewitt / 1963 / Abstract Harmonic Analysis. Vol. I: Structure of topological groups. Integration theory, group representations / Springer-Verlag
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