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References
G. R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc., (3), 25 (1972), 329–340.
A. Atzmon, On the union of sets of synthesis and Ditkin's condition in regular Banach algebras, Bull. Amer. Math. Soc., (N.S.), 2 (1979), 317–320.
G. F. Bachelis and J. E. Gilbert, Banach spaces of compact multipliers and their dual spaces, Math. Z., 125 (1972), 285–297.
_____, Banach algebras with Rider subalgebras, Bull. Inst. Math. Academia Sinica (Taiwan), 7 (1979), 339–347.
W. G. Bade and P. C. Curtis, Jr., The Wedderburn decomposition of commutative Banach algebras, Amer. J. Math., 82 (1960), 851–866.
J. Benedetto, Spectral Synthesis, Academic Press, New York, 1975.
F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York, 1973.
Y. Domar, Closed primary ideals in a class of Banach algebra, Math. Scand., 7 (1959), 109–125.
_____, On the ideal structure of certain Banach algebras, Math. Scand., 14 (1964), 197–212.
_____, Primary ideals in Beurling algebras, Math. Z., 126 (1972), 361–367.
A. Figà -Talamanca and G. I. Gaudry, Multipliers of LP which vanish at infinity, J. Functional Analysis, 7 (1971), 475–486.
S. Friedberg, Closed subalgebras of group algebras, Trans. Amer. Math. Soc., 147 (1970), 117–125.
C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer-Verlag, New York, 1979.
V. P. Gurarii, Harmonic analysis in spaces with a weight, Trans. Moscow Math. Soc., (English translation), (1979, issue 1), 21–75.
H. Helson, On the ideal structure of group algebras, Ark. Mat., 2 (1952), 83–86.
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Volumes I and II, Springer-Verlag, New York, 1963 and 1970.
E. Hewitt and H. S. Zuckerman, Singular measures with absolutely continuous convolution squares, Proc. Cambridge Philos. Soc., 62 (1966), 399–420. Corrigendum, ibid., 63 (1967), 367–368.
J.-P. Kahane, Idempotents and closed subalgebras of A(Z), Function Algebras, Scott Foresman, Chicago 1966, 198–207.
_____, Séries de Fourier Absolument Convergentes, Springer-Verlag, Berlin, 1970.
Y. Katznelson, An Introduction to Harmonic Analysis, John Wiley & Sons, New York, 1968.
R. Kaufman, M-sets and distributions, Astérisque 5 (1973), 225–230.
T. W. Körner, A pseudofunction on a Helson set, I and II, Astérisque 5 (1973), 3–224 and 231–239.
R. Larsen, An Introduction to the Theory of Multipliers, Springer-Verlag, Berlin, 1971.
V. J. Lomonosov, Invariant subspaces for operators commuting with compact operators, Functional Anal. and Appl., 7 (1973), 55–56.
P. Malliavin, Impossibilité de la synthèse spectrale sur les groupes abéliens non compacts, Publ. Math. Inst. Hautes Études Sci. Paris, (1959), 61–68.
H. Mirkil, A counterexample to discrete spectral synthesis, Compositio Math., 14 (1959/60), 269–273.
C. Pearcy and A. L. Shields, A survey of the Lomonosov technique in the theory of invariant subspaces, Topics in Operator Theory, Amer. Math. Soc. Surveys No. 13, (1974), 219–229.
H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Clarendon, Oxford, 1968.
C. Rickart, Banach Algebras, Van Nostrand, New York, 1960.
W. Rudin, Fourier Analysis on Groups, Interscience, New York, 1962.
S. Saeki, An elementary proof of a theorem of Henry Helson, Tôhoku Math. J., 20 (1968), 244–247.
_____, Helson sets which disobey spectral synthesis, Proc. Amer. Math. Soc., 47 (1975), 371–377.
_____, Singular measures having absolutely continuous convolution powers, Illinois J. Math., 21 (1977), 395–412.
L. Schwartz, Sur une propriété de synthèse spectrale dans les groupes non compacts, C. R. Acad. Sci. Ser. A-B, 227 (1948), A424–A426.
J. D. Stegeman, Extension of a theorem of H. Helson, Proc. Int. Cong. Math. Abstracts, Section 5 (1966), 28.
J. L. Taylor, Measure Algebras, Regional Conference Series in Math., No. 16, Amer. Math. Soc., Providence, 1972.
N. Th. Varopoulos, The functions that operate on B0(Γ) of a discrete group, Bull. Soc. Math. France, 93 (1965), 301–321.
_____, Spectral synthesis on spheres, Proc. Camb. Philos. Soc., 62 (1966), 379–387.
N. Wiener and A. Wintner, Fourier-Stieltjes transforms and singular infinite convolutions, Amer. J. Math., 60 (1938), 513–522.
M. Zafran, The spectra of multiplier transformations on the LP spaces, Ann. Math., 103 (1976), 355–374.
_____, The functions operating on multiplier algebras, J. Functional Analysis, 26 (1977), 289–314.
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Bachelis, G.F. (1983). Some radical quotients in harmonic analysis. In: Bachar, J.M., Bade, W.G., Curtis, P.C., Dales, H.G., Thomas, M.P. (eds) Radical Banach Algebras and Automatic Continuity. Lecture Notes in Mathematics, vol 975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064562
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