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Proceedings of the American Mathematical Society

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On spectral synthesis for sets of the form $ E=\overline{{\rm int}(E)}$


Author: David Colella
Journal: Proc. Amer. Math. Soc. 89 (1983), 236-238
MSC: Primary 43A45
MathSciNet review: 712629
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Abstract: The existence of a Helson set disobeying spectral synthesis is combined with the modified Herz criterion to construct a subset $ E$ of the circle such that spectral synthesis holds for $ E$ and fails for $ \partial E$.


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  • [1] Arne Beurling, Local harmonic analysis with some applications to differential operators, Some Recent Advances in the Basic Sciences, Vol. 1 (Proc. Annual Sci. Conf., Belfer Grad. School Sci., Yeshiva Univ., New York, 1962–1964) Belfer Graduate School of Science, Yeshiva Univ., New York, 1966, pp. 109–125. MR 0427956
  • [2] Colin C. Graham and O. Carruth McGehee, Essays in commutative harmonic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 238, Springer-Verlag, New York-Berlin, 1979. MR 550606
  • [3] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR 0152834

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DOI: https://doi.org/10.1090/S0002-9939-1983-0712629-1
Article copyright: © Copyright 1983 American Mathematical Society