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Abstract:

A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert space, reinforcing the idea that this concept of duality solves the question about an appropriate definition of dual fusion frames. It is shown that for overcomplete fusion frames there always exist duals different from the canonical one. Conditions that assure the uniqueness of duals are given. The relation of dual fusion frame systems with dual frames and dual projective reconstruction systems is established. Optimal dual fusion frames for the reconstruction in case of erasures of subspaces, and optimal dual fusion frame systems for the reconstruction in case of erasures of local frame vectors are determined. Examples that illustrate the obtained results are exhibited. © 2014 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:Properties of finite dual fusion frames
Autor:Heineken, S.B.; Morillas, P.M.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, C1428EGA Buenos Aires, Argentina
Instituto de Matemática Aplicada San Luis, Departamento de Matemática, UNSL, Ejército de los Andes 950, 5700 San Luis, Argentina
Palabras clave:Dual fusion frames; Erasures; Frames; Fusion frames; G-frames; Optimal dual fusion frames; Projective reconstruction systems; Linear algebra; Mathematical techniques; Erasures; Frames; Fusion frames; G-frames; Projective reconstruction; Optimization
Año:2014
Volumen:453
Página de inicio:1
Página de fin:27
DOI: http://dx.doi.org/10.1016/j.laa.2014.04.008
Título revista:Linear Algebra and Its Applications
Título revista abreviado:Linear Algebra Its Appl
ISSN:00243795
CODEN:LAAPA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v453_n_p1_Heineken

Referencias:

  • Arefijamaal, A.A., Ghasemi, S., On characterization and stability of alternate dual g-frames (2013) Turkish J. Math., 37, pp. 71-79
  • Casazza, P.G., The art of frame theory (2000) Taiwanese J. Math., 4 (2), pp. 129-202
  • Casazza, P.G., Kutyniok, G., (2012) Finite Frames. Theory and Applications, , Birkhäuser Boston
  • Casazza, P.G., Kutyniok, G., Frames of subspaces (2004) Contemp. Math., 345 VOL., pp. 87-113
  • Casazza, P.G., Kutyniok, G., Robustness of fusion frames under erasures of subspaces and of local frame vectors (2008) Radon Transforms, Geometry and Wavelets, 464 VOL., pp. 149-160. , E.L. Grinberg, D. Larson, P.E.T. Jorgensen, P. Massopust, G. Olafsson, E.T. Quinto, B. Rubi, Contemp. Math. Amer. Math. Soc. Providence, RI
  • Casazza, P.G., Kutyniok, G., Li, S., Fusion frames and distributed processing (2008) Applied and Computational Harmonic Analysis, 25 (1), pp. 114-132. , DOI 10.1016/j.acha.2007.10.001, PII S1063520307001078
  • Christensen, O., (2003) An Introduction to Frames and Riesz Bases, , Birkhäuser Boston
  • Gǎvruţa, P., On the duality of fusion frames (2007) J. Math. Anal. Appl., 333 (2), pp. 871-879
  • Heineken, S.B., Morillas, P.M., Benavente, A.M., Zakowicz, M.I., (2013) Dual Fusion Frames, , arxiv:1308.4595
  • Krishtal, I., Frames, fusion frames, and g-frames - An overview (2011) 9th International Conference on Sampling Theory and Applications (SampTA 2011), , Singapore, May 2-6
  • Leng, J., Han, D., Optimal dual frames for erasures II (2011) Linear Algebra Appl., 435 (6), pp. 1464-1472
  • Lopez, J., Han, D., Optimal dual frames for erasures (2010) Linear Algebra Appl., 432 (1), pp. 471-482
  • Kovačević, J., Chebira, A., An introduction to frames (2008) Found. Trends Signal Process., 2, pp. 1-94
  • Massey, P.G., Optimal reconstruction systems for erasures and for the q-potential (2009) Linear Algebra Appl., 431, pp. 1302-1316
  • Massey, P.G., Ruiz, M.A., Stojanoff, D., Duality in reconstruction systems (2012) Linear Algebra Appl., 436 (3), pp. 447-464
  • Massey, P.G., Ruiz, M.A., Stojanoff, D., Robust dual reconstruction systems and fusion frames (2012) Acta Appl. Math., 119 (1), pp. 167-183
  • Sun, W., G-frames and g-Riesz bases (2006) Journal of Mathematical Analysis and Applications, 322 (1), pp. 437-452. , DOI 10.1016/j.jmaa.2005.09.039, PII S0022247X05009625

Citas:

---------- APA ----------
Heineken, S.B. & Morillas, P.M. (2014) . Properties of finite dual fusion frames. Linear Algebra and Its Applications, 453, 1-27.
http://dx.doi.org/10.1016/j.laa.2014.04.008
---------- CHICAGO ----------
Heineken, S.B., Morillas, P.M. "Properties of finite dual fusion frames" . Linear Algebra and Its Applications 453 (2014) : 1-27.
http://dx.doi.org/10.1016/j.laa.2014.04.008
---------- MLA ----------
Heineken, S.B., Morillas, P.M. "Properties of finite dual fusion frames" . Linear Algebra and Its Applications, vol. 453, 2014, pp. 1-27.
http://dx.doi.org/10.1016/j.laa.2014.04.008
---------- VANCOUVER ----------
Heineken, S.B., Morillas, P.M. Properties of finite dual fusion frames. Linear Algebra Its Appl. 2014;453:1-27.
http://dx.doi.org/10.1016/j.laa.2014.04.008