Abstract:
The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogue to the canonical dual frame. Here a new concept of dual is studied in infinite-dimensional separable Hilbert spaces. It extends the commonly used notion and overcomes these technical difficulties. We show that with this definition in many cases dual fusion frames behave similar to dual frames. We present examples of non-canonical dual fusion frames. © 2014, Springer Basel.
Registro:
Documento: |
Artículo
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Título: | Dual fusion frames |
Autor: | Heineken, S.B.; Morillas, P.M.; Benavente, A.M.; Zakowicz, M.I. |
Filiación: | Departamento de Matemática and IMAS, FCEyN, Universidad de Buenos Aires and CONICET, Pabellón I, Ciudad Universitaria, Buenos Aires, C1428EGA, Argentina Departamento de Matemática and IMASL, FCFMyN, Universidad Nacional de San Luis and CONICET, Ejército de los Andes 950, San Luis, 5700, Argentina Departamento de Matemática and IMASL, FCFMyN, Universidad Nacional de San Luis, Ejército de los Andes 950, San Luis, 5700, Argentina Departamento de Matemática, FCFMyN, Universidad Nacional de San Luis, Ejército de los Andes 950, San Luis, 5700, Argentina
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Palabras clave: | Dual fusion frames; Frames; Fusion frames; Gabor systems |
Año: | 2014
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Volumen: | 103
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Número: | 4
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Página de inicio: | 355
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Página de fin: | 365
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DOI: |
http://dx.doi.org/10.1007/s00013-014-0697-2 |
Título revista: | Archiv der Mathematik
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Título revista abreviado: | Arch. Math.
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ISSN: | 0003889X
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0003889X_v103_n4_p355_Heineken |
Referencias:
- Casazza, P.G., The art of frame theory (2000) Taiwanese Jour. of Math., 4 (2), pp. 129-202
- Casazza, P.G., Kutyniok, G., Frames of subspaces, Contemp (2004) Math, 345, pp. 87-113
- Casazza, P.G., Kutyniok, G., (2012) (Eds.), Finite Frames. Theory and Applications, , Birkhäuser, Boston:
- Casazza, P.G., Kutyniok, G., Li, S., Fusion frames and distributed processing (2008) Appl. Comput. Harmon. Anal, 25, pp. 114-132
- Christensen, O., An introduction to frames and Riesz bases (2003) Appl. Numer. Harmon. Anal.
- Daubechies, I., Ten Lectures on Wavelets, SIAM, Philadelphia (1992) PA
- Duffin, R.J., Schaeffer, A.C., A class of nonharmonic Fourier series (1952) Trans. Amer. Math. Soc., 72, pp. 341-366
- Heineken, S.B., Morillas, P.M., Properties of finite dual fusion frames (2014) Linear Algebra Appl., 453, pp. 1-27
- Ruiz, M.A., Stojanoff, D., Some properties of frames of subspaces obtained by operator theory methods (2008) J. Math. Anal. Appl., 343, pp. 366-378
Citas:
---------- APA ----------
Heineken, S.B., Morillas, P.M., Benavente, A.M. & Zakowicz, M.I.
(2014)
. Dual fusion frames. Archiv der Mathematik, 103(4), 355-365.
http://dx.doi.org/10.1007/s00013-014-0697-2---------- CHICAGO ----------
Heineken, S.B., Morillas, P.M., Benavente, A.M., Zakowicz, M.I.
"Dual fusion frames"
. Archiv der Mathematik 103, no. 4
(2014) : 355-365.
http://dx.doi.org/10.1007/s00013-014-0697-2---------- MLA ----------
Heineken, S.B., Morillas, P.M., Benavente, A.M., Zakowicz, M.I.
"Dual fusion frames"
. Archiv der Mathematik, vol. 103, no. 4, 2014, pp. 355-365.
http://dx.doi.org/10.1007/s00013-014-0697-2---------- VANCOUVER ----------
Heineken, S.B., Morillas, P.M., Benavente, A.M., Zakowicz, M.I. Dual fusion frames. Arch. Math. 2014;103(4):355-365.
http://dx.doi.org/10.1007/s00013-014-0697-2