φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS
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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.
Abstract
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.
참고문헌 (27)
- A. Aldroubi, "p-frames and shift invariant subspaces of Lp", J. Fourier Anal. Appl, 7(1), pp.1~21 (2001)
- C. de Boor, "The structure of nitely generated shift-invariant spaces in L2(Rd)", J. Funct. Anal, 119(1), pp.37~78 (1994)
- P. G. Casazza, "The art of frame theory", Taiwanese J. Math, 4(2), pp.129~201 (2000)
- P. G. Casazza, "Modern tools for Weyl-Heisenberg (Gabor) frame theory", Adv. in Image. and Electron. Physics, 115, pp.1~127 (2001)
- P. G. Casazza, "Weyl-Heisenberg frames for subspaces of L2(R)", Proc. Amer. Math. Soc, 129(1), pp.145~154 (2001)
- P. G. Casazza, "Frames for Banach spaces, The functional and harmonic analysis of wavelets and frames", Contemp. Math, 247, pp.149~182 (1999), Amer. Math. Soc
- P. G. Casazza, "Frames of subspaces, Wavelets, frames and operator theory", Contemp. Math, 345, pp.87~113 (2004), Amer. Math. Soc
- P. G. Casazza, "Bracket products for Weyl-Heisenberg frames, Advances in Gabor analysis", Appl. Numer. Harmon. Anal, pp.71~98 (2003), Birkhauser Boston
- O. Christensen, "An introduction to Frames and Riesz Bases" (2003), Birkhauser
- R. Duffin, "A class of nonharmonic Fourier series", Trans. Amer. Math. Soc, 72, pp.341~366 (1952)
- H. G. Feichtinger, "Gabor Analysis and Algorithms" (1998), Birkhauser
- G. B. Folland, "A Course in Abstract Harmonic Analysis" (1995), CRC Press
- G. B. Folland, "Real Analysis" (1984), John Wiley
- M. Frank, "Frames in Hilbert C*-modules and C*-algebras", J. Operator Theory, 48(2), pp.273~314 (2002)
- E. Hernandez, "A First Course on Wavelets, Studies in Advanced Mathematics" (1996), CRC Press
- E. Hewitt, "Abstract Harmonic Analysis. Vol. I: Structure of topological groups. Integration theory, group representations" (1963), Springer-Verlag
- G. Honnouvo, "Gabor-type frames from generalized Weyl-Heisenberg groups, preprint", ~
- R. A. Kamyabi Gol, "A range function approach to shift-invariant spaces on locally compact Abelian groups", Int. J. Wavelets. Multiresolut. Inf. Process, to appear, ~
- R. A. Kamyabi Gol, "Bracket products on locally compact Abelian groups", J. Sci. Islam. Repub. Iran, 19(2), pp.153~157 (2008)
- R. A. Kamyabi Gol, "φ-Factorable operators and Weyl-Heisenberg frames on LCA groups, preprint", ~
- R. A. Kamyabi Gol, "The structure of shift invariant spaces on a locally compact Abelian group", J. Math. Anal. Appl, 340(1), pp.219~225 (2008)
- E. Kaniuth, "Zeros of the Zak transform on locally compact Abelian groups", Proc. Amer. Math. Soc, 126(12), pp.3561~3569 (1998)
- G. Kutyniok, "Time Frequency Analysis on Locally Compact Groups", 박사, pp.2000
- G. Kutyniok, "The theory of reproducing systems on locally compact Abelian groups", Colloq. Math, 106(2), pp.197~220 (2006)
- A. Ron, "Frames and stable bases for shift-invariant subspaces of L2(Rd)", Canad. J. Math, 47(5), pp.1051~1094 (1995)
- W. Sun, "G-frames and g-Riesz bases", J. Math. Anal. Appl, 322(1), pp.437~452 (2006)
- R. Young, "An Introduction to Nonharmonic Fourier Series" (1980), Academic Press