Relations between the difference spectra of unions and intersections are studied and their implications on some problems in spectral synthesis are observed.
References
K. De Leeuw and C. Herz, “An invariance property of spectral synthesis,” Ill. J. Math., 9, 220–229 (1965).
P. Eymard, “L‘algebre de Fourier d‘un groupe localement compact,” Bull. Soc. Math. France, 92, 181–236 (1964).
C. S. Herz, “Spectral synthesis for the Cantor set,” Proc. Nat. Acad. Sci. USA, 42, 42–43 (1956).
T. K. Muraleedharan and K. Parthasarathy, “On unions and intersections of sets of synthesis,” Proc. Amer. Math. Soc., 123, 1213–1216 (1995).
T. K. Muraleedharan, K. Parthasarathy, and Sujatha Varma, “Nonsynthesizable intersections of sets of synthesis,” Bull. London Math. Soc., 28, 373–374 (1996).
T. K. Muraleedharan and K. Parthasarathy, “Difference spectrum and spectral synthesis,” Tohoku Math. J., 51, 65–73 (1999).
T. K. Muraleedharan, “Weak Wiener–Ditkin sets,” Acta Math. Hung., 133, No. 4, 359–364 (2011).
D. L. Salinger and J. D. Stegeman, “Difference spectra of ideals for nonmetrizable groups,” J. London Math. Soc., 26, 531–540 (1980).
J. D. Stegeman, “Extension of a theorem of H. Helson,” Proc. Int. Congr. Math. Abstr. 5, Moscow (1966).
J. D. Stegeman, “Some problems on spectral synthesis,” Proc. Harmonic Analysis (Iraklion, 1978), Lect. Notes Math., 781 (1980), pp. 194–203.
N. Th. Varopoulos, “Sur les ensembles parfaits et les series trigonometriques,” C. R. Acad. Sci. Ser. A-B, 262, A384–A387 (1966).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 10, pp. 1434–1438, October, 2015.
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Joseph, J., Muraleedharan, T.K. Some Remarks on Spectral Synthesis Sets. Ukr Math J 67, 1611–1617 (2016). https://doi.org/10.1007/s11253-016-1176-7
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DOI: https://doi.org/10.1007/s11253-016-1176-7