Artículo
Barbieri, D.; Cabrelli, C.; Hernández, E.; Luthy, P.; Molter, U.; Mosquera, C. "Frames of exponentials and sub-multitiles in LCA groups " (2018) Comptes Rendus Mathematique. 356(1):107-113
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Abstract:
In this note, we investigate the existence of frames of exponentials for L2(Ω) in the setting of LCA groups. Our main result shows that sub-multitiling properties of Ω⊂Gˆ with respect to a uniform lattice Γ of Gˆ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames. © 2017 Académie des sciences
Registro:
| Documento: | Artículo |
| Título: | Frames of exponentials and sub-multitiles in LCA groups |
| Autor: | Barbieri, D.; Cabrelli, C.; Hernández, E.; Luthy, P.; Molter, U.; Mosquera, C. |
| Filiación: | Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, 28049, Spain Departamento de Matemática, FCEyN, Universidad de Buenos Aires, IMAS-UBA-CONICET, Argentina College of Mount Saint Vincent, Bronx, NY, United States |
| Año: | 2018 |
| Volumen: | 356 |
| Número: | 1 |
| Página de inicio: | 107 |
| Página de fin: | 113 |
| DOI: | http://dx.doi.org/10.1016/j.crma.2017.12.002 |
| Título revista: | Comptes Rendus Mathematique |
| Título revista abreviado: | C. R. Math. |
| ISSN: | 1631073X |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1631073X_v356_n1_p107_Barbieri |
Referencias:
- Agora, E., Antezana, J., Cabrelli, C., Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups (2015) Adv. Math., 285, pp. 454-477
- Barbieri, D., Hernández, E., Mayeli, A., Lattice sub-tilings and frames in LCA groups (2017) C. R. Acad. Sci. Paris, Ser. I, 356 (2), pp. 193-199
- Cabrelli, C., Paternostro, V., Shift-invariant spaces on LCA groups (2010) J. Funct. Anal., 258 (6), pp. 2034-2059
- Feldman, J., Greenleaf, F.P., Existence of Borel transversals in groups (1968) Pac. J. Math., 25, pp. 455-461
- Fuglede, B., Commuting self-adjoint partial differential operators and a group theoretic problem (1974) J. Funct. Anal., 16, pp. 101-121
- Grepstad, S., Lev, N., Multi-tiling and Riesz basis (2014) Adv. Math., 252 (15), pp. 1-6
- Han, D., Kornelson, K., Larson, D., Weber, E., Frames for Undergraduates (2007) Student Mathematical Library, 40. , American Mathematical Society
- Hewitt, E., Ross, K.A., Abstract Harmonic Analysis, Vol. I, Structure of Topological Groups, Integration Theory, Group Representations (1979), 2nd ed. Springer; Kolountzakis, M., Multiple lattice tiles and Riesz bases of exponentials (2015) Proc. Amer. Math. Soc., 143, pp. 741-747
- Pedersen, S., Spectral theory of commuting self-adjoint partial differential operators (1987) J. Funct. Anal., 73, pp. 122-134
- Young, R.M., Introduction to Nonharmonic Fourier Series (1980), Academic Press
Citas:
---------- APA ----------
Barbieri, D., Cabrelli, C., Hernández, E., Luthy, P., Molter, U. & Mosquera, C. (2018) . Frames of exponentials and sub-multitiles in LCA groups . Comptes Rendus Mathematique, 356(1), 107-113.http://dx.doi.org/10.1016/j.crma.2017.12.002
---------- CHICAGO ----------
Barbieri, D., Cabrelli, C., Hernández, E., Luthy, P., Molter, U., Mosquera, C. "Frames of exponentials and sub-multitiles in LCA groups " . Comptes Rendus Mathematique 356, no. 1 (2018) : 107-113.http://dx.doi.org/10.1016/j.crma.2017.12.002
---------- MLA ----------
Barbieri, D., Cabrelli, C., Hernández, E., Luthy, P., Molter, U., Mosquera, C. "Frames of exponentials and sub-multitiles in LCA groups " . Comptes Rendus Mathematique, vol. 356, no. 1, 2018, pp. 107-113.http://dx.doi.org/10.1016/j.crma.2017.12.002
---------- VANCOUVER ----------
Barbieri, D., Cabrelli, C., Hernández, E., Luthy, P., Molter, U., Mosquera, C. Frames of exponentials and sub-multitiles in LCA groups . C. R. Math. 2018;356(1):107-113.http://dx.doi.org/10.1016/j.crma.2017.12.002
