On the Fourier Transformability of Strongly Almost Periodic Measures

In this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their Fourier–Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be the Fourier transform of a measure....

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Published inCanadian journal of mathematics Vol. 72; no. 4; pp. 900 - 927
Main Author Strungaru, Nicolae
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.08.2020
Cambridge University Press
Subjects
Fourier transforms
Mathematics
almost periodic measure
43A25
Fourier transform of measures
43A05
42A75
43A60
Fourier-Bohr series
Eberlein decomposition
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Abstract In this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their Fourier–Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be the Fourier transform of a measure. We discuss the Fourier transformability of a measure on $\mathbb{R}^{d}$ in terms of its Fourier transform as a tempered distribution. We conclude by looking at a large class of such measures coming from the cut and project formalism.
AbstractList In this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their Fourier–Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be the Fourier transform of a measure. We discuss the Fourier transformability of a measure on $\mathbb{R}^{d}$ in terms of its Fourier transform as a tempered distribution. We conclude by looking at a large class of such measures coming from the cut and project formalism.
Abstract In this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their Fourier–Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be the Fourier transform of a measure. We discuss the Fourier transformability of a measure on $\mathbb{R}^{d}$ in terms of its Fourier transform as a tempered distribution. We conclude by looking at a large class of such measures coming from the cut and project formalism.
Author Strungaru, Nicolae
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CitedBy_id crossref_primary_10_1007_s00041_023_10045_z
crossref_primary_10_1016_j_jmaa_2021_125062
crossref_primary_10_1002_mana_202100658
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10.4153/CMB-2011-059-x
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10.1007/978-1-4612-1007-8
10.1090/S0002-9939-2011-11046-3
10.1088/1751-8121/aa5d44
10.1007/978-3-662-04253-3_6
10.1090/tran/7422
10.1007/978-3-642-66128-0
10.1090/proc/12979
10.1017/S1446788700021820
10.1007/s00209-006-0077-0
10.1090/S0002-9939-1955-0068030-2
10.1007/s10955-016-1579-8
10.24033/bsmf.1559
10.1090/S0002-9947-1949-0036455-9
10.1080/14786430802082008
10.1016/j.matpur.2009.05.013
10.1088/1751-8113/46/12/125205
10.1017/S0143385706000800
10.1017/S0143385704000318
10.1007/s00041-005-4021-1
10.4153/CMB-2004-010-8
10.1017/9781139033862
10.1016/0304-4149(79)90007-3
10.1007/978-94-015-8784-6_16
10.1088/1751-8113/47/33/335202
10.1063/1.1609032
10.1307/mmj/1028990025
10.1007/s00023-017-0620-z
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Keywords almost periodic measure
43A25
Fourier transform of measures
43A05
42A75
43A60
Fourier-Bohr series
Eberlein decomposition
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References Lagarias (S0008414X19000075_r18) 2000
S0008414X19000075_r26
S0008414X19000075_r3
S0008414X19000075_r27
S0008414X19000075_r28
S0008414X19000075_r4
Reiter (S0008414X19000075_r32) 2000
S0008414X19000075_r29
S0008414X19000075_r40
S0008414X19000075_r41
S0008414X19000075_r42
S0008414X19000075_r20
S0008414X19000075_r21
S0008414X19000075_r44
S0008414X19000075_r22
S0008414X19000075_r23
S0008414X19000075_r45
Meyer (S0008414X19000075_r25) 1972
Rudin (S0008414X19000075_r37) 1987
Lin (S0008414X19000075_r24) 1969; 79
Argabright (S0008414X19000075_r1) 1974
Eberlein (S0008414X19000075_r15) 1955–56; 3
Gil. de Lamadrid (S0008414X19000075_r19) 1990; 85
S0008414X19000075_r36
S0008414X19000075_r14
S0008414X19000075_r38
S0008414X19000075_r16
S0008414X19000075_r39
S0008414X19000075_r17
Aujogue (S0008414X19000075_r2)
Baake (S0008414X19000075_r7) 2017; 10
Strungaru (S0008414X19000075_r43) 2017
S0008414X19000075_r30
S0008414X19000075_r10
S0008414X19000075_r33
Reiter (S0008414X19000075_r31) 1968
S0008414X19000075_r12
S0008414X19000075_r34
S0008414X19000075_r35
S0008414X19000075_r13
Bourbaki (S0008414X19000075_r11) 1966
S0008414X19000075_r5
S0008414X19000075_r6
Baake (S0008414X19000075_r9) 2004; 573
S0008414X19000075_r8
References_xml – volume: 79
  start-page: 53
  year: 1969
  ident: S0008414X19000075_r24
  article-title: On equivalent norms in the space of square summable entire functions of exponential type
  publication-title: Amer. Math. Soc. Transl. Ser. 2
  contributor:
    fullname: Lin
– ident: S0008414X19000075_r2
  article-title: Pure Point/Continuous Decomposition of Translation-Bounded Measures and Diffraction
  publication-title: Ergodic Theory Dynam. Systems
  contributor:
    fullname: Aujogue
– start-page: 217
  volume-title: Aperiodic order. Vol. 2
  year: 2017
  ident: S0008414X19000075_r43
  contributor:
    fullname: Strungaru
– ident: S0008414X19000075_r3
  doi: 10.1017/CBO9781139025256
– ident: S0008414X19000075_r29
  doi: 10.1017/9781139033862.006
– ident: S0008414X19000075_r38
  doi: 10.1007/s00454-004-1156-9
– volume: 573
  start-page: 61
  year: 2004
  ident: S0008414X19000075_r9
  article-title: Weighted Dirac combs with pure point diffraction
  publication-title: J. Reine Angew. Math.
  contributor:
    fullname: Baake
– ident: S0008414X19000075_r40
  doi: 10.4153/CMB-2011-059-x
– ident: S0008414X19000075_r39
  doi: 10.4153/CJM-2012-032-1
– year: 2000
  ident: S0008414X19000075_r32
  contributor:
    fullname: Reiter
– ident: S0008414X19000075_r30
  doi: 10.1007/978-1-4612-1007-8
– volume: 10
  start-page: 161
  year: 2017
  ident: S0008414X19000075_r7
  article-title: Spectral notions of aperiodic order
  publication-title: Discrete Contin. Dyn. Syst. Ser. S
  contributor:
    fullname: Baake
– ident: S0008414X19000075_r16
  doi: 10.1090/S0002-9939-2011-11046-3
– ident: S0008414X19000075_r35
  doi: 10.1088/1751-8121/aa5d44
– ident: S0008414X19000075_r27
  doi: 10.1007/978-3-662-04253-3_6
– volume: 85
  year: 1990
  ident: S0008414X19000075_r19
  article-title: Almost periodic measures
  publication-title: Mem. Amer. Math. Soc.
  contributor:
    fullname: Gil. de Lamadrid
– ident: S0008414X19000075_r23
  doi: 10.1090/tran/7422
– ident: S0008414X19000075_r10
  doi: 10.1007/978-3-642-66128-0
– ident: S0008414X19000075_r17
  doi: 10.1090/proc/12979
– ident: S0008414X19000075_r36
  doi: 10.1017/S1446788700021820
– ident: S0008414X19000075_r21
  doi: 10.1007/s00209-006-0077-0
– ident: S0008414X19000075_r14
  doi: 10.1090/S0002-9939-1955-0068030-2
– ident: S0008414X19000075_r44
  doi: 10.1007/s10955-016-1579-8
– volume-title: Real and complex analysis
  year: 1987
  ident: S0008414X19000075_r37
  contributor:
    fullname: Rudin
– year: 1974
  ident: S0008414X19000075_r1
  contributor:
    fullname: Argabright
– ident: S0008414X19000075_r12
  doi: 10.24033/bsmf.1559
– ident: S0008414X19000075_r13
  doi: 10.1090/S0002-9947-1949-0036455-9
– ident: S0008414X19000075_r20
  doi: 10.1080/14786430802082008
– start-page: 61
  volume-title: Directions in mathematical quasicrystals
  year: 2000
  ident: S0008414X19000075_r18
  contributor:
    fullname: Lagarias
– year: 1972
  ident: S0008414X19000075_r25
  contributor:
    fullname: Meyer
– ident: S0008414X19000075_r22
  doi: 10.1016/j.matpur.2009.05.013
– ident: S0008414X19000075_r41
  doi: 10.1088/1751-8113/46/12/125205
– ident: S0008414X19000075_r8
  doi: 10.1017/S0143385706000800
– ident: S0008414X19000075_r5
  doi: 10.1017/S0143385704000318
– ident: S0008414X19000075_r6
  doi: 10.1007/s00041-005-4021-1
– volume-title: Clasical harmonic analysis and locally compact groups
  year: 1968
  ident: S0008414X19000075_r31
  contributor:
    fullname: Reiter
– ident: S0008414X19000075_r28
  doi: 10.4153/CMB-2004-010-8
– ident: S0008414X19000075_r4
  doi: 10.1017/9781139033862
– volume-title: General topology. parts I and II
  year: 1966
  ident: S0008414X19000075_r11
  contributor:
    fullname: Bourbaki
– ident: S0008414X19000075_r45
  doi: 10.1016/0304-4149(79)90007-3
– ident: S0008414X19000075_r26
  doi: 10.1007/978-94-015-8784-6_16
– ident: S0008414X19000075_r42
  doi: 10.1088/1751-8113/47/33/335202
– ident: S0008414X19000075_r33
  doi: 10.1063/1.1609032
– volume: 3
  start-page: 137
  year: 1955–56
  ident: S0008414X19000075_r15
  article-title: The point spectrum of weakly almost periodic functions
  publication-title: Michigan Math. J.
  doi: 10.1307/mmj/1028990025
  contributor:
    fullname: Eberlein
– ident: S0008414X19000075_r34
  doi: 10.1007/s00023-017-0620-z
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Snippet In this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their Fourier–Bohr...
Abstract In this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their...
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SubjectTerms Fourier transforms
Mathematics
Title On the Fourier Transformability of Strongly Almost Periodic Measures
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