Abstract
It is proved that the one-sided Wiener’s Theorem does not hold for the motion group SO(N)⋊R N. That is, there exists a proper closed right ideal inL 1(SO(N)⋊R N) which is not contained in any closed maximal right ideal.
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References
L. Ehrenpreis and F. I. Mautner,Some properties of the Fourier transform on semisimple Lie groups III, Trans. Am. Math. Soc.90(1959), 431–484.
R. Gangolli,On the symmetry of L 1 algebras of locally compact motion groups and the Wiener Tauberian Theorem, J. Funct. Anal.25(1977), 244–252.
H. Leptin,Ideal theory in group algebras of locally compact groups, Invent. Math.31(1976), 259–278.
H. Leptin,On one-sided harmonic analysis in non-commutative locally compact groups, J. Reine Angew. Math.306(1979), 122–153.
M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1971.
N. T. Varopoulos,Spectral synthesis on spheres, Proc. Camb. Phil. Soc.62(1966), 379–387.
N. I. Vilenkin,Special Functions and the Theory of Group Representations, “Nauka”, Moscow, 1965 (Russian).
Y. Weit,On the one-sided Wiener’s Theorem for the motion group, Ann. of Math.111 (1980), 415–422.
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Weit, Y. On the one-sided Wiener’s Theorem for the motion group onR N . Israel J. Math. 55, 111–120 (1986). https://doi.org/10.1007/BF02772699
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DOI: https://doi.org/10.1007/BF02772699