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Algebras of Smooth Functions

The following sources are recommended by a professor whose research specialty is algebras of smooth functions.


Six Superlative Sources

· E.M. Dyn'kin and L.G. Hanin, Spectral synthesis of ideals in Zygmund algebras: The asymptotic Cauchy problem approach, Michigan Math. J., v. 43, 1996, pp. 539-557.

· L.G. Hanin, Closed ideals in algebras of smooth functions, Dissertationes Mathematicae, v. 371, 1998, pp. 1-67.

· L.G. Hanin, A theorem on spectral synthesis of ideals for a class of Banach algebras, Soviet Math. Doklady, v. 35, no. 1, 1987, pp. 108-112.

· L.I. Hedberg, Spectral synthesis in Sobolev spaces and uniqueness of solutions of the Dirichlet problem, Acta Math. v. 147, 1981, pp. 237-264.

· B. Malgrange, Ideals of Differentiable Functions, Oxford University Press, 1966.

· H. Whitney, On ideals of differentiable functions, Amer. J. Math., v. 70, 1948, pp. 635-658.

Other Excellent Sources

· J.J. Benedetto, Spectral Synthesis, New York, 1975.

· A. Beurling, On the spectral synthesis of bounded functions, Acta Math., v. 81, 1949, pp. 225-238.

· A. Beurling, Sur les spectres des fonctions, Analyse Harmonique, Colloques Internationaux du Centre National de la Recherche Scientifique, Paris, 1949, pp. 9-29.

· J. Bruna, Spectral synthesis in non quasi-analytic classes of infinitely differentiable functions, Bull. Sci. Math., 2-e serie, v. 104, 1980, pp. 65-78.

· G. Glaeser, Synthèse spectrale des ideaux de fonctions lipschitziennes, C. R. Acad. Sci. Paris, v. 260, no. 6, 1965, pp. 1539-1542.

· L.I. Hedberg and T.H. Wolff, Thin sets in nonlinear potential theory, Ann. Inst. Fourier, v. 33, no. 4, 1983, pp. 161-187.

· P. Malliavin, Sur l'impossibilité de la synthèse spectrale dans une algèbre de fonctions presque périodique, C. R. Acad. Sci. Paris, v. 248, 1959, pp. 1756-1759.

· P. Malliavin, Sur l'impossibilité de la synthèse spectrale sur la droite, C. R. Acad. Sci. Paris, v. 248, 1959, pp. 2155-2157.

· P. Malliavin, Impossibilité de la synthèse spectrale sur le groupes abéliens non compacts, Publications Mathématiques de l'Institut des Hautes Études Scientifiques Paris, v. 2, 1959, pp. 61-68.

· L. Schwartz, Théorie génerale des fonctions moyenne-périodique, Ann. of Math., v. 48, 1947, pp. 857-929.

· L. Schwartz, Sur une proprieté de synthèse spectrale dans les groupes non compacts, C. R. Acad. Sci. Paris, v. 227, 1948, pp. 424-426.

· D.R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc., v. 111, no. 2, 1964, pp. 240-272.

· G.E. Shilov, On regular normed rings, Trudy Mat. Inst. Steklova, v. 21, 1947, pp. 1-118 (in Russian).

· L. Waelbroeck, Closed ideals of Lipschitz functions, in: Proceedings Int. Symp. "Function Algebras," F. Birtel (ed.), Scott-Foresmann, 1966, pp. 322-325.

· H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., v. 36, 1934, pp. 63-89.

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