Shift generated dual frames for locally compact abelian groups
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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.
Abstract
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.
참고문헌 (18)
- A. Ahmadi, "Shift invariant spaces for local fields", Int. J. Wavelets Multiresolut. Inf. Process, 9(3), pp.417~426 (2011)
- A. Ahmadi, "A characterization of shift invariant spaces on LCA group G with a compact open subgroup"
- J. J. Benedetto, "A wavelet theory for local fields and related groups", J. Geom. Anal, 14(3), pp.423~456 (2004)
- R. L. Benedetto, "Examples of wavelets for local fields, Wavelets, frames and operator theory", Contemp. Math, 345, pp.27~47 (2004), Amer. Math. Soc
- M. Bownik, "The structure of shift invariant subspaces of L2(Rn)", J. Funct. Anal, 177(2), pp.282~309 (2000)
- O. Christensen, "An Introduction to Frames and Riesz Bases" (2003), Birkhauser
- I. Daubechies, "Painless nonorthogonal expansion", J. Math. Phys, 27(5), pp.1271~1283 (1986)
- R. J. Duffin, "A class of nonharmonic Fourier series", Trans. Amer. Math. Soc, 72, pp.341~366 (1952)
- G. B. Folland, "A Course in Abstract Harmonic Analysis" (1995), CRC Press
- P. H. Frampton, "P-adic string N-point function", Phys. Rev. Lett. B, 60, pp.484~486 (1988)
- H. Helson, "Lectures on Invariant Subspaces" (1964), Academic Press
- A. A. Hemmat, "The uniqueness of shift-generated duals for frames in shift-invariant subspaces", J. Fourier Anal. Appl, 13(5), pp.589~606 (2007)
- E. Hewitt, "Abstract Harmonic Analysis. Vol. I: Structure of Topological Groups. Integration Theory, Group Representations" (1963), Springer
- R. A. Kamyabi Gol, "The structure of shift invariant spaces on locally compact abelian group", J. Math. Anal. Appl, 340, pp.219~225 (2008)
- R. A. Kamyabi Gol, "A range function approach to shift invariant spaces on locally compact abelian group", Int. J. Wavelets Multiresolut. Inf. Process, 8(1), pp.49~59 (2010)
- N. J. Munch, "Noise reduction in tight Weyl-Heisenberg frames", IEEE Trans. Inform. Theory, 38(2), pp.608~616 (1992)
- H. Reiter, "Classical Harmonic Analysis and Locally Compact Groups" (2000), Clarendon Press
- W. Rudin, "Real and Complex Analysis" (1987), McGraw-Hill Co