WOVEN g-FRAMES IN HILBERT C*-MODULES
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Woven frames are motivated from distributed signal processing with potential applications in wireless sensor networks. g-frames provide more choices on analyzing functions from the frame expansion coefficients. The objective of this paper is to introduce woven g-frames in Hilbert C∗-modules, and to develop its fundamental properties. In this investigation, we establish sufficient conditions under which two g-frames possess the weaving properties. We also investigate the sufficient conditions under which a family of g-frames possess weaving properties.
Abstract
Woven frames are motivated from distributed signal processing with potential applications in wireless sensor networks. g-frames provide more choices on analyzing functions from the frame expansion coefficients. The objective of this paper is to introduce woven g-frames in Hilbert C∗-modules, and to develop its fundamental properties. In this investigation, we establish sufficient conditions under which two g-frames possess the weaving properties. We also investigate the sufficient conditions under which a family of g-frames possess weaving properties.
참고문헌 (20)
- L. Arambaic, "On frames for countably generated Hilbert C ∗-modules", Proc. Amer. Math. Soc, 135, pp.469~478 (2007)
- T. Bemrose, "Weaving frames", Oper. Matrices, 10(4), pp.1093~1116 (2016)
- H. Bolcskei, "Frame-theoretic analysis of oversampled filter banks", IEEE Trans. Signal Process, 46(12), pp.3256~3268 (1998)
- J. S. Byrnes, "Mathematics for multimedia signal processing II : Discrete finite frames and signal reconstruction", Signals Processing for Multimedia, 174, pp.35~54 (1999)
- E. J. Candes, "New tight frames of curvelets and optimal representations of objects with piecewise C 2singularities", Commun. Pure Appl. Math, 57(2), pp.219~266 (2004)
- P. G. Casazza, "Fusion frames and distributed processing", Appl. Comput. Harmon. Anal, 25, pp.114~132 (2008)
- P. G. Casazza, "Weaving properties of Hilbert space frames", Sampling Theory and Applications (SampTA), pp.110~114 (2015), IEEE
- P. G. Casazza, "Weaving Schauder frames", J. Approx. Theory, 211, pp.42~60 (2016)
- I. Daubechies, "Painless nonorthogonal expansions", J. Math. Phys, 27, pp.1271~1283 (1986)
- R. J. Duffin, "A class of nonharmonic Fourier series", Trans. Amer. Math. Soc, 72, pp.341~366 (1952)
- Y. C. Eldar, "Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors", J. Fourier. Anal. Appl, 9(1), pp.77~96 (2003)
- M. Frank, "Frames in Hilbert C*-modules and C*-algebras", J. Operator Theory, 48, pp.273~314 (2002)
- F. Ghobadzadeh, "Woven frames in Hilbert C ∗-modules", J. Comput. Anal. Appl, 25, pp.1220~1232 (2018)
- I. Kaplansky, "Algebra of type I", Annals of Math, 56, pp.460~472 (1952)
- A. Khosravi, "Fusion frames and g-frames in Hilbert C*-modules", Int. J. Wavelets Multiresol. Inf. Process, 6, pp.433~466 (2008)
- S. Li, "Pseudoframes for subspaces with applications", J. Fourier Anal. Appl, 10(4), pp.409~431 (2004)
- D. Li, "On weaving g-frames for Hilbert spaces", Complex Anal. Oper. Theory, 14(2), pp.1~25 (2017)
- W. Paschke, "Inner product modules over B∗-algebras", Trans. Amer. Math. Soc, 182, pp.443~468 (1973)
- T. Strohmer, "Grassmanian frames with applications to coding and communi-cations", Appl. Comput. Harmon. Anal, 14, pp.257~275 (2003)
- W. Sun, "G-frames and g-Riesz bases", J. Math. Anal. Appl, 322(1), pp.437~452 (2006)
