Book contents
- Frontmatter
- Contents
- Contributors
- Foreword by Jeffrey C. Lagarias
- Preface
- Chapter 1 More Inflation Tilings
- Chapter 2 Discrete Tomography of Model Sets: Reconstruction and Uniqueness
- Chapter 3 Geometric Enumeration Problems for Lattices and Embedded ℤ-Modules
- Chapter 4 Almost Periodic Measures and their Fourier Transforms
- Chapter 5 Almost Periodic Pure Point Measures
- Chapter 6 Averaging Almost Periodic Functions along Exponential Sequences
- Epilogue. Gateways Towards Quasicrystals
- Index
- References
Chapter 4 - Almost Periodic Measures and their Fourier Transforms
Published online by Cambridge University Press: 26 October 2017
Book contents
- Frontmatter
- Contents
- Contributors
- Foreword by Jeffrey C. Lagarias
- Preface
- Chapter 1 More Inflation Tilings
- Chapter 2 Discrete Tomography of Model Sets: Reconstruction and Uniqueness
- Chapter 3 Geometric Enumeration Problems for Lattices and Embedded ℤ-Modules
- Chapter 4 Almost Periodic Measures and their Fourier Transforms
- Chapter 5 Almost Periodic Pure Point Measures
- Chapter 6 Averaging Almost Periodic Functions along Exponential Sequences
- Epilogue. Gateways Towards Quasicrystals
- Index
- References
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- Aperiodic Order , pp. 173 - 270Publisher: Cambridge University PressPrint publication year: 2017
References
[AO1] and (2013) Aperiodic Order. Vol. 1: A Mathematical Invitation (Cambridge University Press, Cambridge).
[1] and (1974) Fourier analysis of unbounded measures on locally compact Abelian groups, Memoirs Amer. Math. Soc., no. 145 (AMS, Providence, RI).
[2] (1972) On the mean of a weakly almost periodic function,
Proc. Amer. Math. Soc.
36, 315–316.Google Scholar
[3] and (2004) Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra,
Ergodic Th. & Dynam. Syst.
24, 1867–1893. arXiv:math.DS/0302231.CrossRefGoogle Scholar
[4] and (2017) Spectral notions of aperiodic order,
Discr. Cont. Dynam. Syst. S
10, 161–190. arXiv:1601.06629.Google Scholar
[5] and (1975) Potential Theory on Locally Compact Abelian Groups (Springer, Berlin).
[6] (1947) Almost Periodic Functions, English edition (Chelsea, New York).
[7] (1965) Intègration, Chapters III and IV (Hermann, Paris).
[8] (1966) General Topology, parts I and II (Hermann, Paris).
[9] (1967) Intègration, Chapter V (Hermann, Paris).
[11] (2013) Measure Theory, 2nd ed. (Birkhäuser, Boston).
[12] (1970) Treatise on Analysis, vol. II (Academic Press, New York).
[13] and (1968) Linear Operators. Part I: General Theory (Interscience, New York).
[14] (1947) Weak compactness in Banach spaces I,
Proc. Nat. Acad. Sci. USA
33, 51–53.CrossRefGoogle Scholar
[15] (1949) Abstract ergodic theorems and weak almost periodic functions,
Trans. Amer. Math. Soc.
67, 217–240.CrossRefGoogle Scholar
[16] (1955) A note on Fourier–Stieltjes transforms,
Proc. Amer. Math. Soc.
6, 310–312.CrossRefGoogle Scholar
[17] (1955/56). The point spectrum of weakly almost periodic functions, Michigan Math. J.
3, 137–139.Google Scholar
[18] (2012) Bohr and Besicovitch almost periodic discrete sets and quasicrystals,
Proc. Amer. Math. Soc.
140, 1761–1767. arXiv:1011.4036.Google Scholar
[19] and (1990) Almost periodic measures, Memoirs Amer. Math. Soc.
85, no. 428 (AMS, Providence, RI.
[20] (2005) Quasicrystals and almost periodicity,
Commun. Math. Phys.
255, 665–681. arXiv:math-ph/0212012.Google Scholar
[21] (1995) On diffraction by aperiodic structures,
Commun. Math. Phys.
169, 25–43.CrossRefGoogle Scholar
[22] (1997) Diffraction by aperiodic structures. In The Mathematics of Longrange Aperiodic Order,
eds., NATO ASI Series C 489, pp. 239–268 (Kluwer, Dordrecht).
[23] (1975) General Topology, GTM 27, reprint (Springer, New York).
[24] (2002) Functional Analysis (Wiley, New York).
[25] (2009) Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks,
Commun. Math. Phys.
87, 225–258. arXiv:math.ph/0608026.Google Scholar
[26] and (2007) Pure point diffraction and cut and project schemes for measures: The smooth case,
Math. Z.
256, 347–378. arXiv:math.DS/0603453.CrossRefGoogle Scholar
[27] and (2009) Pure point spectrum for measure dynamical systems on locally compact Abelian groups,
J. Math. Pures Appl.
92, 323–341. arXiv:0704.2498.CrossRefGoogle Scholar
[28] and (2016) On weakly almost periodic measures, Preprint arXiv:1609.08219.
[29] and (2015) Quasicrystals and Poisson's summation formula,
Invent. Math.
200, 585–606. arXiv:1312.6884.Google Scholar
[30] (2012) Quasicrystals,almost periodic patterns,mean-periodic functions and irregular sampling,
African Diaspora J. Math.
13, 7–45.Google Scholar
[31] (2016) Measures with locally finite support and spectrum,
Proc. Nat. Acad. Sci. USA
113, 3152–3158.CrossRefGoogle Scholar
[32] (1997) Meyer sets and their duals. In The Mathematics of Long-Range Aperiodic Order,
eds., NATO ASI Series C 489, pp. 403–441 (Kluwer, Dordrecht).
[33] (2017) A general framework for tilings, Delone sets, functions and measures, and their interrelation, Preprint arXiv:1702.03807.
[34] (1943) On weakly compact subsets of a Banach space,
Amer. J. Math.
65, 108–136.CrossRefGoogle Scholar
[35] (1995) Analysis Now, rev. printing (Springer, New York).
[36] (2014) Eberlein–˘Smulian Theorem and Some of Its Applications, Master's thesis (Department of Mathematics, University of Agder).
[37] and (1980) Methods of Modern Mathematical Physics I: Functional Analysis, 2nd ed. (Academic Press, San Diego, CA).
[38] and (2000) Classical Harmonic Analysis and Locally Compact Groups (Clarendon Press, Oxford).
[39] and (2015) Pure point diffraction and Poisson summation, Preprint arXiv:1512.00912.
[40] and (2017) A short guide to pure point diffraction in cutand- project sets,
J. Phys. A: Math. Theor.
50, 154003 (25pp). arXiv:1606.08831.Google Scholar
[41] (1962) Fourier Analysis on Groups (Wiley, New York).
[42] (1987) Real and Complex Analysis, 3rd ed (McGraw–Hill, New York).
[43] (1991) Functional Analysis, 2nd ed. (McGraw–Hill, New York).
[44] (2000) Generalised model sets and dynamical systems. In Directions in Mathematical Quasicrystals,
and eds., CRM Monograph Series, vol. 13, pp. 143–159 (AMS, Providence, RI).
[45] (1973) Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures (Oxford University Press, Oxford).
[46] (2017) Almost periodic pure point measures. In Aperiodic Order. Vol. 2: Crystallography and Almost Periodicity (this volume),
and eds., pp. 271–342 (Cambridge University Press, Cambridge).
[47] (2017) On the Fourier transformability of strongly almost periodic measures, Preprint arXiv:1704.04778.
[48] and (2016) Diffraction theory and almost periodic distributions,
J. Stat. Phys.
164, 1183–1216. arXiv:1603.04796.CrossRefGoogle Scholar
[49] (1979) Mengentheoretische Topologie, 2nd ed. (Springer, Berlin).
[50] (1953) L'intègration dans les groupes topologiques et ses applications, 2nd ed. (Hermann, Paris).
[51] (1967) An elementary proof of the Eberlein–˘Smulian theorem,
Math. Ann.
172, 116–118.Google Scholar
[53] (1980) Functional Analysis, SCSM 123, 6th ed. (Springer, Berlin).
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