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

Colella, David

doi:10.1090/S0002-9939-1983-0712629-1

On spectral synthesis for sets of the form $E=\overline {\textrm {int}(E)}$
HTML articles powered by AMS MathViewer

by David Colella

Proc. Amer. Math. Soc. 89 (1983), 236-238

DOI: https://doi.org/10.1090/S0002-9939-1983-0712629-1

PDF | Request permission

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 $\partial E$.

References

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) Yeshiva Univ., Belfer Graduate School of Science, New York, 1966, pp. 109–125. MR 0427956
Colin C. Graham and O. Carruth McGehee, Essays in commutative harmonic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 238, Springer-Verlag, New York-Berlin, 1979. MR 550606, DOI 10.1007/978-1-4612-9976-9
Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834