Linear combinations of generators in multiplicatively invariant spaces
Multiplicatively invariant (MI) spaces are closed subspaces of L2(ω, H) that are invariant under multiplication by (some) functions in L∞(ω); they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of func...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Instytut Matematyczny
2015
|
| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 06949caa a22007217a 4500 | ||
|---|---|---|---|
| 001 | PAPER-13658 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204403.0 | ||
| 008 | 190411s2015 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84926347964 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Paternostro, V. | |
| 245 | 1 | 0 | |a Linear combinations of generators in multiplicatively invariant spaces |
| 260 | |b Instytut Matematyczny |c 2015 | ||
| 270 | 1 | 0 | |m Paternostro, V.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Argentina |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Aldroubi, A., Gröchenig, K., Nonuniform sampling and reconstruction in shiftinvariant spaces (2001) SIAM Rev., 43, pp. 585-620 | ||
| 504 | |a Antezana, J., Corach, G., Ruiz, M., Stojanoff, D., Nullspaces and frames (2005) J. Math. Anal. Appl., 309, pp. 709-723 | ||
| 504 | |a Barbieri, D., Hernández, E., Parcet, J., Riesz and frame systems generated by unitary actions of discrete groups (2014) Appl. Comput. Harmon. Anal., , online | ||
| 504 | |a Barbieri, D., Hernández, E., Paternostro, V., (2014) The Zak Transform and the Structure of Spaces Invariant under the Action of An LCA Group, , preprint | ||
| 504 | |a Bownik, M., The structure of shift-invariant subspaces of L2(ℝn) (2000) J. Funct. Anal., 177, pp. 282-309 | ||
| 504 | |a Bownik, M., Kaiblinger, N., Minimal generator sets for finitely generated shiftinvariant subspaces of L2(ℝn) (2006) J. Math. Anal. Appl., 313, pp. 342-352 | ||
| 504 | |a Bownik, M., Ross, K.A., (2014) The Structure of Translation-invariant Spaces on Locally Compact Abelian Groups, , preprint | ||
| 504 | |a Cabrelli, C., Mosquera, C., Paternostro, V., Linear combination of frame generators in systems of translates (2014) J. Math. Anal. Appl., 413, pp. 776-788 | ||
| 504 | |a Cabrelli, C., Paternostro, V., Shift-invariant spaces on LCA groups (2010) J. Funct. Anal., 258, pp. 2034-2059 | ||
| 504 | |a Cabrelli, C., Paternostro, V., Shift-modulation invariant spaces on LCA groups (2012) Studia Math., 211, pp. 1-19 | ||
| 504 | |a De Boor, C., Devore, R.A., Ron, A., Approximation from shift-invariant subspaces of L2(ℝd) (1994) Trans. Amer. Math. Soc., 341, pp. 787-806 | ||
| 504 | |a De Boor, C., Devore, R.A., Ron, A., The structure of finitely generated shiftinvariant spaces in L2(ℝd) (1994) J. Funct. Anal., 119, pp. 37-78 | ||
| 504 | |a Deutsch, F., The angle between subspaces of a Hilbert space, in: Approximation Theory, Wavelets and Applications (1995) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454, pp. 107-130. , (Maratea 1994), Kluwer, Dordrecht | ||
| 504 | |a Gröchenig, K., Localization of frames, banach frames, and the invertibility of the frame operator (2004) J. Fourier Anal. Appl., 10, pp. 105-132 | ||
| 504 | |a Havin, V.P., Jöricke, B., The uncertainty principle in harmonic analysis (1995) Commutative Harmonic Analysis III, Encyclopaedia Math. Sci., 72, pp. 177-259. , Springer, Berlin+261-266 | ||
| 504 | |a Helson, H., (1964) Lectures on Invariant Subspaces, , Academic Press New York | ||
| 504 | |a Hernández, E., Šikic, 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 Hernández, E., Weiss, G., (1996) A First Course on Wavelets, , CRC Press, Boca Raton, FL | ||
| 504 | |a Kamyabi Gol, R.A., Raisi Tousi, R., A range function approach to shift-invariant spaces on locally compact abelian groups (2010) Int. J. Wavelets Multiresolut. Inf. Process., 8, pp. 49-59 | ||
| 504 | |a Kato, T., (1976) Perturbation Theory for Linear Operators, , Springer New York | ||
| 504 | |a Mackey, G.W., Induced representations of locally compact groups i (1952) Ann. of Math., 55, pp. 101-139 | ||
| 504 | |a Mallat, S.G., Multiresolution approximations and wavelet orthonormal bases of L2(ℝ) (1989) Trans. Amer. Math. Soc., 315, pp. 69-87 | ||
| 504 | |a Ron, A., Shen, Z., Frames and stable bases for shift-invariant subspaces of L2(ℝd) (1995) Canad. J. Math., 47, pp. 1051-1094 | ||
| 504 | |a Rudin, W., (1962) Fourier Analysis on Groups, , Interscience, New York | ||
| 504 | |a Srinivasan, T.P., Doubly invariant subspaces (1964) Pacific J. Math., 14, pp. 701-707 | ||
| 504 | |a Sun, Q., Local reconstruction for sampling in shift-invariant spaces (2010) Adv. Comput. Math., 32, pp. 335-352 | ||
| 504 | |a Sun, W., Sampling theorems for multivariate shift invariant subspaces (2005) Sampl. Theory Signal Image Process., 4, pp. 73-98 | ||
| 504 | |a Zhao, P., Zhao, C., Casazza, P.G., Perturbation of regular sampling in shiftinvariant spaces for frames (2006) IEEE Trans. Inform. Theory, 52, pp. 4643-4648 | ||
| 520 | 3 | |a Multiplicatively invariant (MI) spaces are closed subspaces of L2(ω, H) that are invariant under multiplication by (some) functions in L∞(ω); they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of functions constructed by taking linear combinations of the generators of a finitely generated MI space is a new set of generators for the same space, and we give necessary and sufficient conditions on the linear combinations to preserve frame properties. We then apply our results on MI spaces to systems of translates in the context of locally compact abelian groups and we extend some results previously proven for systems of integer translates in L2(ℝd). © Instytut Matematyczny PAN, 2015. |l eng | |
| 536 | |a Detalles de la financiación: Alexander von Humboldt-Stiftung | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Buenos Aires, 1428, Argentina | ||
| 593 | |a IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina | ||
| 690 | 1 | 0 | |a FIBERS |
| 690 | 1 | 0 | |a FRAME |
| 690 | 1 | 0 | |a GRAMIAN |
| 690 | 1 | 0 | |a LCA GROUPS |
| 690 | 1 | 0 | |a MULTIPLICATIVELY INVARIANT SPACES |
| 690 | 1 | 0 | |a RANGE FUNCTIONS |
| 690 | 1 | 0 | |a SHIFT INVARIANT SPACE |
| 773 | 0 | |d Instytut Matematyczny, 2015 |g v. 226 |h pp. 1-16 |k n. 1 |p Stud. Math. |x 00393223 |w (AR-BaUEN)CENRE-251 |t Studia Mathematica | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-84926347964&doi=10.4064%2fsm226-1-1&partnerID=40&md5=456e3fec8a2e07ccc3c057afc5d636eb |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.4064/sm226-1-1 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00393223_v226_n1_p1_Paternostro |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v226_n1_p1_Paternostro |y Registro en la Biblioteca Digital |
| 961 | |a paper_00393223_v226_n1_p1_Paternostro |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 74611 | ||