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Abstract:

We prove the existence of Riesz bases of exponentials of L2(Ω), provided that Ω ⊂ ℝd is a measurable set of finite and positive measure, not necessarily bounded, that satisfies a multi-tiling condition and an arithmetic property that we call admissibility. This property is satisfied for any bounded domain, so our results extend the known case of bounded multi-tiles. We also extend known results for submulti-tiles and frames of exponentials to the unbounded case. © 2018 American Mathematical Society.

Registro:

Documento: Artículo
Título:Riesz bases of exponentials on unbounded multi-tiles
Autor:Cabrelli, C.; Carbajal, D.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Instituto de Matemática “Luis Santaló” (IMAS-CONICET-UBA), Buenos Aires, Argentina
Palabras clave:Frames of exponentials; Multi-tiling; Paley-wiener spaces; Riesz bases of exponentials; Shift-invariant spaces; Submulti- tiling
Año:2018
Volumen:146
Número:5
Página de inicio:1991
Página de fin:2004
DOI: http://dx.doi.org/10.1090/proc/13980
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v146_n5_p1991_Cabrelli

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
  • Alexeev, B., Cahill, J., Mixon, D.G., Full spark frames (2012) J. Fourier Anal. Appl., 18 (6), pp. 1167-1194
  • Bownik, M., The structure of shift-invariant subspaces of L2 (Rn) (2000) J. Funct. Anal., 177 (2), pp. 282-309
  • Barbieri, D., Cabrelli, C., Hernández, E., Luthy, P., Molter, U., Mosquera, C., (2018) C. R. Math. Acad. Sci, , Paris, to appear
  • Barbieri, D., Hernández, E., Mayeli, A., Lattice sub-tilings and frames in LCA groups (2017) C. R. Math. Acad. Sci. Paris, 355 (2), pp. 193-199
  • Cabrelli, C., Paternostro, V., Shift-invariant spaces on LCA groups (2010) J. Funct. Anal., 258 (6), pp. 2034-2059
  • Farkas, B., Matolcsi, M., Móra, P., On Fuglede’s conjecture and the existence of universal spectra (2006) J. Fourier Anal. Appl., 12 (5), pp. 483-494
  • Farkas, B., Révész, S.G., Tiles with no spectra in dimension 4 (2006) Math. Scand., 98 (1), pp. 44-52
  • Fuglede, B., Commuting self-adjoint partial differential operators and a group theoretic problem (1974) J. Functional Analysis, 16, pp. 101-121
  • Grepstad, S., Lev, N., Multi-tiling and Riesz bases (2014) Adv. Math., 252, pp. 1-6
  • Helson, H., (1964) Lectures on invariant subspaces, , Academic Press, New York-London
  • Iosevich, A., Fuglede conjecture for lattices, , www.math.rochester.edu/people/faculty/iosevich/expository/FugledeLattice.pdf, preprint available at
  • Iosevich, A., Katz, N., Tao, T., The Fuglede spectral conjecture holds for convex planar domains (2003) Math. Res. Lett., 10 (5-6), pp. 559-569
  • Kozma, G., Nitzan, S., Combining Riesz bases (2015) Invent. Math., 199 (1), pp. 267-285
  • Kozma, G., Nitzan, S., Combining Riesz bases in Rd (2016) Rev. Mat. Iberoam., 32 (4), pp. 1393-1406
  • Kolountzakis, M.N., Multiple lattice tiles and Riesz bases of exponentials (2015) Proc. Amer. Math. Soc., 143 (2), pp. 741-747
  • Kolountzakis, M.N., Matolcsi, M., Tiles with no spectra (2006) Forum Math., 18 (3), pp. 519-528
  • Kolountzakis, M.N., Non-symmetric convex domains have no basis of exponentials (2000) Illinois J. Math., 44 (3), pp. 542-550
  • Matei, B., Meyer, Y., Simple quasicrystals are sets of stable sampling (2010) Complex Var. Elliptic Equ., 55 (8-10), pp. 947-964
  • Matei, B., Meyer, Y., Quasicrystals are sets of stable sampling (2008) C. R. Math. Acad. Sci. Paris, 346 (23-24), pp. 1235-1238. , English, with English and French summaries
  • Nitzan, S., Olevskii, A., Ulanovskii, A., Exponential frames on unbounded sets (2016) Proc. Amer. Math. Soc., 144 (1), pp. 109-118
  • Seip, K., (2004) Interpolation and sampling in spaces of analytic functions, 33. , University Lecture Series, American Mathematical Society, Providence, RI
  • Tao, T., Fuglede’s conjecture is false in 5 and higher dimensions (2004) Math. Res. Lett., 11 (2-3), pp. 251-258
  • Tao, T., An uncertainty principle for cyclic groups of prime order (2005) Math. Res. Lett., 12 (1), pp. 121-127
  • Young, R.M., (2001) An introduction to nonharmonic Fourier series, , 1st ed., Academic Press, Inc., San Diego, CA

Citas:

---------- APA ----------
Cabrelli, C. & Carbajal, D. (2018) . Riesz bases of exponentials on unbounded multi-tiles. Proceedings of the American Mathematical Society, 146(5), 1991-2004.
http://dx.doi.org/10.1090/proc/13980
---------- CHICAGO ----------
Cabrelli, C., Carbajal, D. "Riesz bases of exponentials on unbounded multi-tiles" . Proceedings of the American Mathematical Society 146, no. 5 (2018) : 1991-2004.
http://dx.doi.org/10.1090/proc/13980
---------- MLA ----------
Cabrelli, C., Carbajal, D. "Riesz bases of exponentials on unbounded multi-tiles" . Proceedings of the American Mathematical Society, vol. 146, no. 5, 2018, pp. 1991-2004.
http://dx.doi.org/10.1090/proc/13980
---------- VANCOUVER ----------
Cabrelli, C., Carbajal, D. Riesz bases of exponentials on unbounded multi-tiles. Proc. Am. Math. Soc. 2018;146(5):1991-2004.
http://dx.doi.org/10.1090/proc/13980