Critical pairs of sequences of a mixed frame potential

The classical frame potential in a finite-dimensional Hilbert space has been introduced by Benedetto and Fickus, who showed that all finite unit-norm tight frames can be characterized as the minimizers of this energy functional. This was the starting point of a series of new results in frame theory,...

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Autor principal: Carrizo, I.
Otros Autores: Heineken, S.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Taylor and Francis Inc. 2014
Acceso en línea:Registro en Scopus
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030 |a NFAOD 
100 1 |a Carrizo, I. 
245 1 0 |a Critical pairs of sequences of a mixed frame potential 
260 |b Taylor and Francis Inc.  |c 2014 
270 1 0 |m Heineken, S.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS-CONICET, C1428EGA C.A.B.A, Buenos Aires, Argentina; email: sigrid.heineken@gmail.com 
506 |2 openaire  |e Política editorial 
504 |a Benedetto, J., Colella, D., Wavelet analysis of spectogram seizure chips (1995) Proc. SPIE Conf. on Wavelet Applications in Signal and Image Proceedings, pp. 512-521. , San Diego, CA, July 
504 |a Benedetto, J., Fickus, M., Finite normalized tight frames (2003) Adv. Comput. Math., 18, pp. 357-385 
504 |a Casazza, P., Custom building finite frames (2004) Contemp. Math., Amer. Math. Soc., 345, pp. 61-86 
504 |a Casazza, P., Fickus, M., Kovacević, J., Leon, M., Tremain, J., (2006) A Physical Interpretation of Tight Frames, , Applied Numerical Harmonics and Analysis, Birkhäuser, Boston 
504 |a Casazza, P., Fickus, M., Minimizing fusion frame potential (2009) Acta. Appl. Math., 107 (103), pp. 7-24 
504 |a Christensen, O., (2003) An Introduction to Frames and Riesz Basis, , Birkhäuser, Boston 
504 |a Christensen, O., Eldar, Y., Generalized shift-invariant systems and frames for subspaces (2005) J. Fourier Anal. Appl., 11 (3), pp. 299-311 
504 |a Christensen, O., Powell, A.M., Xiao, X.C., A note on finite dual frame pairs (2012) Proc. Amer. Math. Soc., 140, pp. 3921-3930 
504 |a Daubechies, I., The wavelet transform, time-frequency localization and signal analysis (1990) IEEE Trans. Inform. Th., 36 (5), pp. 961-1005 
504 |a Daubechies, I., (1992) Ten Lectures on Wavelets, , SIAM, Philadelphia 
504 |a Duffin, R.J., Schaeffer, A.C., A class of nonharmonic Fourier series (1952) Trans. Amer. Math. Soc., 72, pp. 341-366 
504 |a Goyal, V., Kovacević, J., Kelner, J., Quantized frame expansions with erasures (2001) Appl. Comput. Harmon. Anal., 10, pp. 203-233 
504 |a Massey, P., Ruiz, M., Stojanoff, D., The structure of minimizers of the frame potential on fusion frames (2010) J. Fourier Anal. Appl., 16 (4), pp. 514-543 
504 |a Heil, C., Walnut, D., Continuous and discrete wavelet transforms (1989) SIAM Rev., 31, pp. 628-666 
504 |a Strohmer, T., Heath Jr., R., Grassmanian frames with applications to coding and communications (2003) Appl. Comput. Harmon. Anal., 14 (3), pp. 257-275 
504 |a Waldron, S., Generalized Welch bound equality sequences are tight frames (2003) IEEE Trans. Info. Th., 49 (9), pp. 2307-2309 
520 3 |a The classical frame potential in a finite-dimensional Hilbert space has been introduced by Benedetto and Fickus, who showed that all finite unit-norm tight frames can be characterized as the minimizers of this energy functional. This was the starting point of a series of new results in frame theory, related to finding tight frames with determined lengths. The frame potential has been studied in the traditional setting as well as in the finite-dimensional fusion frame context. In this work we introduce the concept of mixed frame potential, which generalizes the notion of the Benedetto-Fickus frame potential. We study properties of this new potential, and give the structure of its critical pairs of sequences on a suitable restricted domain. For a given sequence {m } m=1.. N in K, where K is or , we obtain necessary and sufficient conditions in order to have a dual pair of frames {f m m=1. N, {g m } m=1.. N such that f m, g m = m for all m = 1.. N. copy; 2014 Copyright Taylor & Francis Group, LLC.  |l eng 
536 |a Detalles de la financiación: Seventh Framework Programme, PICT 2011-0436, PIEF-GA-2008-221090, UBACyT 2011-2014 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica 
536 |a Detalles de la financiación: Universidad Nacional de San Luis 
536 |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas 
536 |a Detalles de la financiación: S. Heineken acknowledges the support of the Intra-European Marie Curie Fellowship (FP7 project PIEF-GA-2008-221090), UBACyT 2011-2014 (UBA) and PICT 2011-0436 (ANPCyT). 
536 |a Detalles de la financiación: I. Carrizo was supported by the EUCETIFA project of the University of Vienna, CONICET, Universidad Nacional de San Luis and the Technical University of Denmark. 
593 |a NuHAG, Faculty of Mathematics, University of Vienna, Vienna, Austria 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS-CONICET, C1428EGA C.A.B.A, Buenos Aires, Argentina 
690 1 0 |a DUAL FRAMES 
690 1 0 |a FINITE FRAMES 
690 1 0 |a FRAME POTENTIAL 
690 1 0 |a LAGRANGE MULTIPLIERS 
690 1 0 |a FUNCTIONAL ANALYSIS 
690 1 0 |a MATHEMATICAL TECHNIQUES 
690 1 0 |a DUAL FRAMES 
690 1 0 |a ENERGY FUNCTIONALS 
690 1 0 |a FINITE FRAMES 
690 1 0 |a FRAME POTENTIAL 
690 1 0 |a FRAME THEORY 
690 1 0 |a FUSION FRAMES 
690 1 0 |a NEW RESULTS 
690 1 0 |a RESTRICTED-DOMAIN 
690 1 0 |a LAGRANGE MULTIPLIERS 
700 1 |a Heineken, S. 
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