Subspaces with extra invariance nearest to observed data

Applied and Computational Harmonic Analysis - Tập 41 - Trang 660-676 - 2016
C. Cabrelli1,2, C.A. Mosquera1,2
1Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
2IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina

Tài liệu tham khảo

Aldroubi, 2011, A dimension reduction scheme for the computation of optimal unions of subspaces, Sampl. Theory Signal Image Process., 10, 135, 10.1007/BF03549538 Aldroubi, 2007, Optimal shift invariant spaces and their Parseval frame generators, Appl. Comput. Harmon. Anal., 23, 273, 10.1016/j.acha.2007.05.001 Aldroubi, 2010, Invariance of a shift-invariant space, J. Fourier Anal. Appl., 16, 60, 10.1007/s00041-009-9068-y Aldroubi, 2008, Optimal non-linear models for sparsity and sampling, J. Fourier Anal. Appl., 14, 793, 10.1007/s00041-008-9040-2 Aldroubi, 2001, Nonuniform sampling and reconstruction in shift-invariant spaces, SIAM Rev., 43, 585, 10.1137/S0036144501386986 Aldroubi, 2012, Principal shift-invariant spaces with extra invariance nearest to observed data, Collect. Math., 63, 393, 10.1007/s13348-011-0047-7 Aldroubi, 2011, On the existence of optimal unions of subspaces for data modeling and clustering, Found. Comput. Math., 11, 363, 10.1007/s10208-011-9086-4 Anastasio, 2011, Invariance of a shift-invariant space in several variables, Complex Anal. Oper. Theory, 5, 1031, 10.1007/s11785-010-0045-x Bownik, 2000, The structure of shift-invariant subspaces of L2(Rn), J. Funct. Anal., 177, 282, 10.1006/jfan.2000.3635 Cabrelli, 2010, Shift-invariant spaces on LCA groups, J. Funct. Anal., 258, 2034, 10.1016/j.jfa.2009.11.013 Christensen, 2003, An introduction to frames and Riesz bases, 10.1007/978-0-8176-8224-8_6 de Boor, 1994, Approximation from shift-invariant subspaces of L2(Rd), Trans. Amer. Math. Soc., 341, 787 de Boor, 1994, The structure of finitely generated shift-invariant spaces in L2(Rd), J. Funct. Anal., 119, 37, 10.1006/jfan.1994.1003 Grepstad, 2014, Multi-tiling and Riesz bases, Adv. Math., 252, 1, 10.1016/j.aim.2013.10.019 Gröchenig, 2001, Foundations of time-frequency analysis, 10.1007/978-1-4612-0003-1_3 Heil, 2011, A basis theory primer, 10.1007/978-0-8176-4687-5 Helson, 1964 Hernández, 1996, A First Course on Wavelets, 10.1201/9780367802349 Kolountzakis, 2015, Multiple lattice tiles and Riesz bases of exponentials, Proc. Amer. Math. Soc., 143, 741, 10.1090/S0002-9939-2014-12310-0 Mallat, 1989, Multiresolution approximations and wavelet orthonormal bases of L2(R), Trans. Amer. Math. Soc., 315, 69 Ron, 1995, Frames and stable bases for shift-invariant subspaces of L2(Rd), Canad. J. Math., 47, 1051, 10.4153/CJM-1995-056-1 Tessera, 2014, Uncertainty principles in finitely generated shift-invariant spaces with additional invariance, J. Math. Anal. Appl., 410, 134, 10.1016/j.jmaa.2013.07.077