Exponential frames on unbounded sets
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- by Shahaf Nitzan, Alexander Olevskii and Alexander Ulanovskii PDF
- Proc. Amer. Math. Soc. 144 (2016), 109-118 Request permission
Abstract:
For every set $S$ of finite measure in $\mathbb {R}$ we construct a discrete set of real frequencies $\Lambda$ such that the exponential system $\{\exp (i\lambda t),\lambda \in \Lambda \}$ is a frame in $L^2(S)$.References
- Joshua Batson, Daniel A. Spielman, and Nikhil Srivastava, Twice-Ramanujan sparsifiers, SIAM Rev. 56 (2014), no. 2, 315–334. MR 3201185, DOI 10.1137/130949117
- A. Beurling, Balayage of Fourier–Stieltjes Transforms, The collected Works of Arne Beurling. Vol. 2, Harmonic Analysis. Birkhauser, Boston 1989.
- N. J. A. Harvey and N. Olver, Pipage rounding, pessimistic estimators and matrix concentration, Proc. of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms (2014), 926–945. ISBN: 978-1-611973-38-9.
- H. J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967), 37–52. MR 222554, DOI 10.1007/BF02395039
- A. Marcus, D. A. Spielman, and N. Srivastava. Interlacing families II: Mixed characteristic polynomials and the Kadison-Singer problem, Annals of Mathematics, 182, 2015. To appear.
- Shahaf Nitzan, Alexander Olevskii, and Alexander Ulanovskii, A few remarks on sampling of signals with small spectrum, Tr. Mat. Inst. Steklova 280 (2013), no. Ortogonal′nye Ryady, Teoriya Priblizheniĭ i Smezhnye Voprosy, 247–254; English transl., Proc. Steklov Inst. Math. 280 (2013), no. 1, 240–247. MR 3241849, DOI 10.1134/s0081543813010173
- Shahaf Nitzan and Alexander Olevskii, Revisiting Landau’s density theorems for Paley-Wiener spaces, C. R. Math. Acad. Sci. Paris 350 (2012), no. 9-10, 509–512 (English, with English and French summaries). MR 2929058, DOI 10.1016/j.crma.2012.05.003
- Alexander Olevskii and Alexander Ulanovskii, Uniqueness sets for unbounded spectra, C. R. Math. Acad. Sci. Paris 349 (2011), no. 11-12, 679–681 (English, with English and French summaries). MR 2817390, DOI 10.1016/j.crma.2011.05.010
- Joaquim Ortega-Cerdà and Kristian Seip, Fourier frames, Ann. of Math. (2) 155 (2002), no. 3, 789–806. MR 1923965, DOI 10.2307/3062132
- Robert M. Young, An introduction to nonharmonic Fourier series, 1st ed., Academic Press, Inc., San Diego, CA, 2001. MR 1836633
Additional Information
- Received by editor(s): November 10, 2014
- Published electronically: September 4, 2015
- Communicated by: Alexander Iosevich
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 109-118
- MSC (2010): Primary 42A38, 42C15, 94A12
- DOI: https://doi.org/10.1090/proc/12868
- MathSciNet review: 3415581