Group Riesz and frame sequences: the Bracket and the Gramian
Given a discrete group and a unitary representation on a Hilbert space H, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of H. As a consequence, combining this result with known frame theory, we can recover all previous Bracket characterizations of Riesz and fr...
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Springer-Verlag Italia s.r.l.
2018
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| LEADER | 06357caa a22007217a 4500 | ||
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| 001 | PAPER-25213 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205714.0 | ||
| 008 | 190410s2018 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85044952238 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Barbieri, D. | |
| 245 | 1 | 0 | |a Group Riesz and frame sequences: the Bracket and the Gramian |
| 260 | |b Springer-Verlag Italia s.r.l. |c 2018 | ||
| 270 | 1 | 0 | |m Barbieri, D.; Universidad Autónoma de MadridSpain; email: davide.barbieri@uam.es |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Barbieri, D., Hernández, E., Parcet, J., Riesz and frame systems generated by unitary actions of discrete groups (2014) Appl. Comput. Harmon. Anal., 39, pp. 369-399 | ||
| 504 | |a Barbieri, D., Hernández, E., Paternostro, V., The Zak transform and the structure of spaces invariant by the action of an LCA group (2015) J. Funct. Anal., 269, pp. 1327-1358 | ||
| 504 | |a Benedetto, J.J., Li, S., Multiresolution analysis frames with applications (1993) ICASSP’93, 3, pp. 304-307. , Minneapolis | ||
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| 504 | |a Benedetto, J.J., Li, S., The theory of multiresolution analysis frames and applications to filter banks (1998) Appl. Comput. Harmon. Anal., 5, pp. 389-427 | ||
| 504 | |a Bownik, M., The structure of shift-invariant subspaces of L2(Rn) (2000) J. Funct. Anal., 177 (2), pp. 282-309 | ||
| 504 | |a Christensen, O., (2003) An introduction to frames and Riesz bases, , Birkhäuser, Basel | ||
| 504 | |a Connes, A., (1994) Noncommutative Geometry, , Academic Press, Cambridge | ||
| 504 | |a Conway, J.B., (1990) A Course in Functional Analysis, , 2, Springer, Berlin | ||
| 504 | |a Conway, J.B., (2000) A Course in Operator Theory, , AMS, Providence | ||
| 504 | |a Daubechies, I., (1992) Ten Lectures on Wavelets, , SIAM, New Delhi | ||
| 504 | |a de Boor, C., DeVore, R.A., Ron, A., Approximation from shift invariant subspaces of L2(Rd) (1994) Trans. Am. Math. Soc., 341, pp. 787-806 | ||
| 504 | |a de Boor, C., DeVore, R.A., Ron, A., The structure of finitely generated shift-invariant spaces in L2(Rd) (1994) J. Funct. Anal., 119, pp. 37-78 | ||
| 504 | |a Folland, G.B., (1995) A Course in Abstract Harmonic Analysis, , CRC Press, Boca Raton | ||
| 504 | |a Halmos, P.R., (1951) Introduction to Hilbert Spaces and the Theory of Spectral Multiplicity, , Chelsea Publishing Company, London | ||
| 504 | |a Heil, C.E., Powell, A.M., Gabor Schauder bases and the Balian–Low theorem (2006) J. Math. Phys., 47, pp. 1-21 | ||
| 504 | |a Hernández, E., Weiss, G., (1996) A First Course on Wavelets, , CRC Press, Boca Raton | ||
| 504 | |a Hernández, E., Šikić, H., Weiss, G., Wilson, E., Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform (2010) Colloq. Math., 118, pp. 313-332 | ||
| 504 | |a Junge, M., Mei, T., Parcet, J., Smooth Fourier multipliers on group von Neumann algebras (2014) Geom. Funct. Anal., 24, pp. 1913-1980 | ||
| 504 | |a Kadison, R.V., Ringrose, J.R., (1983) Fundamentals of the Theory of Operator Algebras, Vol. 1 and 2, , Academic Press, Cambridge | ||
| 504 | |a Kubrusly, C.S., (2011) The Elements of Operator Theory, , 2, Birkhäuser, Basel | ||
| 504 | |a Meyer, Y., (1992) Wavelets and Operators, , Cambridge University Press, Cambridge | ||
| 504 | |a Nelson, E., Notes on non-commutative integration (1974) J. Funct. Anal., 15, pp. 103-116 | ||
| 504 | |a Pisier, G., Xu, Q., Non-Commutative Lp spaces (2003) Handbook of the Geometry of Banach Spaces, Chapter 34, 2. , Johnson WB, Lindenstrauss J, (eds), Elsevier, Amsterdam | ||
| 504 | |a Rudin, W., (1973) Functional Analysis, , McGraw-Hill Book Company, New York City | ||
| 504 | |a Takesaki, M., (2003) Theory of Operator Algebras, Vol. 1 and 2, , Springer, Berlin | ||
| 504 | |a Terp, M., (1981) Lp -spaces associated with von Neumann Algebras, , Copenhagen University, Copenhagen | ||
| 520 | 3 | |a Given a discrete group and a unitary representation on a Hilbert space H, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of H. As a consequence, combining this result with known frame theory, we can recover all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation. © 2017, Universitat de Barcelona. |l eng | |
| 536 | |a Detalles de la financiación: Ministerio de Economía y Competitividad | ||
| 536 | |a Detalles de la financiación: Acknowledgements D. Barbieri was supported by a Marie Curie Intra European Fellowship (Prop. N. 626055) within the 7th European Community Framework Programme. D. Barbieri and E. Hernández were supported by Grants MTM2013-40945-P and MTM2016-76566-P (Ministerio de Economía y Competitividad, Spain). V. Paternostro by Grants UBACyT 2002013010022BA and 20020150200037BA, and CONICET-PIP 11220110101018. | ||
| 593 | |a Universidad Autónoma de Madrid, Madrid, 28049, Spain | ||
| 593 | |a Universidad de Buenos Aires and IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, 1428, Argentina | ||
| 690 | 1 | 0 | |a BRACKET MAP |
| 690 | 1 | 0 | |a GRAMIAN OPERATOR |
| 690 | 1 | 0 | |a GROUP VON NEUMANN ALGEBRAS |
| 690 | 1 | 0 | |a INVARIANT SUBSPACES |
| 690 | 1 | 0 | |a RIESZ AND FRAME SEQUENCES |
| 700 | 1 | |a Hernández, E. | |
| 700 | 1 | |a Paternostro, V. | |
| 773 | 0 | |d Springer-Verlag Italia s.r.l., 2018 |g v. 69 |h pp. 221-236 |k n. 2 |p Collect. Math. |x 00100757 |t Collectanea Mathematica | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s13348-017-0202-x |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00100757_v69_n2_p221_Barbieri |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v69_n2_p221_Barbieri |y Registro en la Biblioteca Digital |
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