Book Review
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MathSciNet review:
3855022
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Book Information:
Authors:
Alexander M. Olevskii and
Alexander Ulanovskii
Title:
Functions with disconnected spectrum: Sampling, interpolation, translates
Additional book information:
University Lecture Series, Vol. 65,
American Mathematical Society,
Providence, RI,
2016,
x+138 pp.,
ISBN 978-1-4704-2889-1
Joaquim Bruna, Alexander Olevskii, and Alexander Ulanovskii, Completeness in $L^1(\Bbb R)$ of discrete translates, Rev. Mat. Iberoam. 22 (2006), no. 1, 1–16. MR 2267311, DOI 10.4171/RMI/447
R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341–366. MR 47179, DOI 10.1090/S0002-9947-1952-0047179-6
Gerald B. Folland and Alladi Sitaram, The uncertainty principle: a mathematical survey, J. Fourier Anal. Appl. 3 (1997), no. 3, 207–238. MR 1448337, DOI 10.1007/BF02649110
Alex Iosevich, Nets Katz, and Terence Tao, The Fuglede spectral conjecture holds for convex planar domains, Math. Res. Lett. 10 (2003), no. 5-6, 559–569. MR 2024715, DOI 10.4310/MRL.2003.v10.n5.a1
M. Ĭ. Kadec′, The exact value of the Paley-Wiener constant, Dokl. Akad. Nauk SSSR 155 (1964), 1253–1254 (Russian). MR 0162088
Jean-Pierre Kahane, Sur les fonctions moyenne-périodiques bornées, Ann. Inst. Fourier (Grenoble) 7 (1957), 293–314 (French). MR 102702
Gady Kozma and Shahaf Nitzan, Combining Riesz bases, Invent. Math. 199 (2015), no. 1, 267–285. MR 3294962, DOI 10.1007/s00222-014-0522-3
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
Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava, Interlacing families II: Mixed characteristic polynomials and the Kadison-Singer problem, Ann. of Math. (2) 182 (2015), no. 1, 327–350. MR 3374963, DOI 10.4007/annals.2015.182.1.8
Basarab Matei and Yves Meyer, Simple quasicrystals are sets of stable sampling, Complex Var. Elliptic Equ. 55 (2010), no. 8-10, 947–964. MR 2674875, DOI 10.1080/17476930903394689
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
Shahaf Nitzan, Alexander Olevskii, and Alexander Ulanovskii, Exponential frames on unbounded sets, Proc. Amer. Math. Soc. 144 (2016), no. 1, 109–118. MR 3415581, DOI 10.1090/proc/12868
Alexander Olevskiĭ, Completeness in $L^2(\mathbf R)$ of almost integer translates, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), no. 9, 987–991 (English, with English and French summaries). MR 1451238, DOI 10.1016/S0764-4442(97)87873-1
Alexander Olevskiĭ and Alexander Ulanovskii, Universal sampling and interpolation of band-limited signals, Geom. Funct. Anal. 18 (2008), no. 3, 1029–1052. MR 2439002, DOI 10.1007/s00039-008-0674-7
Joaquim Ortega-Cerdà and Kristian Seip, Fourier frames, Ann. of Math. (2) 155 (2002), no. 3, 789–806. MR 1923965, DOI 10.2307/3062132
B. S. Pavlov, The basis property of a system of exponentials and the condition of Muckenhoupt, Dokl. Akad. Nauk SSSR 247 (1979), no. 1, 37–40 (Russian). MR 545940
Kristian Seip, Density theorems for sampling and interpolation in the Bargmann-Fock space, Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 2, 322–328. MR 1136138, DOI 10.1090/S0273-0979-1992-00290-2
Kristian Seip, Beurling type density theorems in the unit disk, Invent. Math. 113 (1993), no. 1, 21–39. MR 1223222, DOI 10.1007/BF01244300
Terence Tao, Fuglede’s conjecture is false in 5 and higher dimensions, Math. Res. Lett. 11 (2004), no. 2-3, 251–258. MR 2067470, DOI 10.4310/MRL.2004.v11.n2.a8
References
- Joaquim Bruna, Alexander Olevskii, and Alexander Ulanovskii, Completeness in $L^1(\mathbb {R})$ of discrete translates, Rev. Mat. Iberoam. 22 (2006), no. 1, 1–16. MR 2267311, DOI 10.4171/RMI/447
- R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341–366. MR 0047179, DOI 10.2307/1990760
- Gerald B. Folland and Alladi Sitaram, The uncertainty principle: a mathematical survey, J. Fourier Anal. Appl. 3 (1997), no. 3, 207–238. MR 1448337, DOI 10.1007/BF02649110
- Alex Iosevich, Nets Katz, and Terence Tao, The Fuglede spectral conjecture holds for convex planar domains, Math. Res. Lett. 10 (2003), no. 5-6, 559–569. MR 2024715, DOI 10.4310/MRL.2003.v10.n5.a1
- M. Ĭ. Kadec′, The exact value of the Paley-Wiener constant, Dokl. Akad. Nauk SSSR 155 (1964), 1253–1254 (Russian). MR 0162088
- Jean-Pierre Kahane, Sur les fonctions moyenne-périodiques bornées, Ann. Inst. Fourier, Grenoble 7 (1957), 293–314 (French). MR 0102702
- Gady Kozma and Shahaf Nitzan, Combining Riesz bases, Invent. Math. 199 (2015), no. 1, 267–285. MR 3294962, DOI 10.1007/s00222-014-0522-3
- H. J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967), 37–52. MR 0222554, DOI 10.1007/BF02395039
- Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava, Interlacing families II: Mixed characteristic polynomials and the Kadison-Singer problem, Ann. of Math. (2) 182 (2015), no. 1, 327–350. MR 3374963, DOI 10.4007/annals.2015.182.1.8
- Basarab Matei and Yves Meyer, Simple quasicrystals are sets of stable sampling, Complex Var. Elliptic Equ. 55 (2010), no. 8-10, 947–964. MR 2674875, DOI 10.1080/17476930903394689
- 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
- Shahaf Nitzan, Alexander Olevskii, and Alexander Ulanovskii, Exponential frames on unbounded sets, Proc. Amer. Math. Soc. 144 (2016), no. 1, 109–118. MR 3415581, DOI 10.1090/proc/12868
- Alexander Olevskiĭ, Completeness in $L^2(\mathbf {R})$ of almost integer translates, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), no. 9, 987–991 (English, with English and French summaries). MR 1451238, DOI 10.1016/S0764-4442(97)87873-1
- Alexander Olevskiĭand Alexander Ulanovskii, Universal sampling and interpolation of band-limited signals, Geom. Funct. Anal. 18 (2008), no. 3, 1029–1052. MR 2439002, DOI 10.1007/s00039-008-0674-7
- Joaquim Ortega-Cerdà and Kristian Seip, Fourier frames, Ann. of Math. (2) 155 (2002), no. 3, 789–806. MR 1923965, DOI 10.2307/3062132
- B. S. Pavlov, The basis property of a system of exponentials and the condition of Muckenhoupt, Dokl. Akad. Nauk SSSR 247 (1979), no. 1, 37–40 (Russian). MR 545940
- Kristian Seip, Density theorems for sampling and interpolation in the Bargmann-Fock space, Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 2, 322–328. MR 1136138, DOI 10.1090/S0273-0979-1992-00290-2
- Kristian Seip, Beurling type density theorems in the unit disk, Invent. Math. 113 (1993), no. 1, 21–39. MR 1223222, DOI 10.1007/BF01244300
- Terence Tao, Fuglede’s conjecture is false in 5 and higher dimensions, Math. Res. Lett. 11 (2004), no. 2-3, 251–258. MR 2067470, DOI 10.4310/MRL.2004.v11.n2.a8
Review Information:
Reviewer:
Mishko Mitkovski
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, South Carolina
Email:
mmitkov@clemson.edu
Journal:
Bull. Amer. Math. Soc.
55 (2018), 553-560
DOI:
https://doi.org/10.1090/bull/1593
Published electronically:
August 16, 2017
Review copyright:
© Copyright 2017
American Mathematical Society
