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Let G be a metrizable, σ-compact locally compact abelian group with a compact open subgroup. In this paper we de ne the Gramian and the dual Gramian operators for shift invariant subspaces of L2(G)and we use them to characterize shift generated dual frames for shift in-variant spaces, which forms a frame for a subspace of L2(G). We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.
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참고문헌 (18)
참고문헌 신청
A. A. Hemmat / 2007 / The uniqueness of shift-generated duals for frames in shift-invariant subspaces / J. Fourier Anal. Appl 13 (5) : 589 ~ 606
A. Ahmadi / / A characterization of shift invariant spaces on LCA group G with a compact open subgroup
A. Ahmadi / 2011 / Shift invariant spaces for local fields / Int. J. Wavelets Multiresolut. Inf. Process 9 (3) : 417 ~ 426
E. Hewitt / 1963 / Abstract Harmonic Analysis. Vol. I: Structure of Topological Groups. Integration Theory, Group Representations / Springer
G. B. Folland / 1995 / A Course in Abstract Harmonic Analysis / CRC Press
A. Ahmadi / / A characterization of shift invariant spaces on LCA group G with a compact open subgroup
A. Ahmadi / 2011 / Shift invariant spaces for local fields / Int. J. Wavelets Multiresolut. Inf. Process 9 (3) : 417 ~ 426
E. Hewitt / 1963 / Abstract Harmonic Analysis. Vol. I: Structure of Topological Groups. Integration Theory, Group Representations / Springer
G. B. Folland / 1995 / A Course in Abstract Harmonic Analysis / CRC Press
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