On the minimizers of the fusion frame potential
We study the minimizers of the fusion frame potential in the case that both the weights and the dimensions of the subspaces are fixed and not necessarily equal. Using a concept of irregularity we provide a description of the local (that are also global) minimizers which projections are eigenoperator...
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| Otros Autores: | , |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Wiley-VCH Verlag
2018
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | We study the minimizers of the fusion frame potential in the case that both the weights and the dimensions of the subspaces are fixed and not necessarily equal. Using a concept of irregularity we provide a description of the local (that are also global) minimizers which projections are eigenoperators of the fusion frame operator. This result will be related to the existence of tight fusion frames. In this way we generalize results known for the classical vector frame potential. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim |
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| Bibliografía: | Benedetto, J.J., Fickus, M., Finite normalized tight frames (2003) Adv. Comput. Math., 18, pp. 357-385 Carrizo, I., Heineken, S., Critical pairs of sequences of a mixed frame potential (2014) Numer. Funct. Anal. Optim., 35, pp. 665-684 Casazza, P.G., Fickus, M., Minimizing fusion frame potential (2009) Acta Appl. Math., 107, pp. 7-24 Casazza, P.G., A physical interpretation of tight frames, Harmonic Analysis and Applications (2006) Appl. Numer. Harmon. Anal., pp. 51-76. , Birkhäuser Boston, Boston Casazza, P.G., Kutyniok, G., Finite frames. Theory and applications (2012) Appl. Numer. Harmon. Anal., , (eds.), Birkhäuser, Boston Casazza, P.G., Kutyniok, G., Frames of subspaces (2004) Contemp. Math., 345, pp. 87-113 Casazza, P.G., Kutyniok, G., Li, S., Fusion frames and distributed processing (2008) Appl. Comput. Harmon. Anal., 25, pp. 114-132 Christensen, O., (2003) An introduction to frames and Riesz bases, , Birkhäuser, Boston Fickus, M., Convolutional frames and the frame potential (2005) Appl. Comput. Harmon. Anal., 19, pp. 77-91 Johnson, B.D., Okoudjou, K.A., Frame potential and finite abelian groups (2008) Contemp. Math., 464, pp. 137-148 Kovačević, J., Chebira, A., An introduction to frames (2008) Found. Trends Signal Process., 2, pp. 1-94 Massey, P.G., Ruiz, M.A., Stojanoff, D., The structure of the minimizers of the frame potential on fusion frames (2010) J. Fourier Anal. Appl., 16, pp. 514-543 |
| ISSN: | 0025584X |
| DOI: | 10.1002/mana.201500493 |