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References
Alexander, H., Uniform algebras on curves, B.A.M.S. 75 (1969), 1269–1272.
Alexander, H., Polynomial approximation and analytic structure, to appear.
Alexander, H., Polynomial approximation and hulls of sets of finite linear measure in ℂn, to appear.
Bishop, E., Subalgebras of functions on a Riemann surface, Pacific J. Math. 8 (1958), 29–50.
Bishop, E., Analyticity in certain Banach algebras, T.A.M.S. 102 (1962), 507–544.
Bishop, E., Holomorphic completions, analytic continuations and the interpolation of seminorms, Ann. Math. 78 (1963), 468–500.
Bjork, J.-E., Relatively maximal function algebras generated by polynomials on compact sets in the complex plane, Arkiv för Mat. 8 (1969), 17–23.
Bjork, J.-E., Analytic structures, papers from the Summer Gathering on Function Algebras at Aarhus, July 1969, 19–28.
Bjork, J.-E., On analytic structures in the maximal ideal space of a function algebra, Papers from the Summer Gathering on Function Algebras at Aarhus, July 1969, 29–35.
Browder, A., Introduction to Function Algebras, Benjamin, 1969.
Chirka, E. M., Approximation of continuous functions by functions holomorphic on Jordan arcs in ℂn, Dokl. Acad. Nauk. SSSR 167 (1966), 38–40. Soviet Math. Dokl. 7 (1966), 336–338.
Gamelin, T. W., Uniform Algebras, Prentice-Hall, 1969.
Gamelin, T. W., Uniform algebras containing the polynomials, preprint.
Gamelin, T. W., and Wilken, D., Closed partitions of maximal ideal spaces, Ill. J. Math. 13 (1969), 789–795.
Gokhberg, I. C., and Krein, M. G., Fundamental aspects of defect numbers, root numbers and indexes of linear operators, Uspehi Mat. Nauk. 12 (1957), No. 2(74), 43–118, A.M.S. Transl. (2) 13 (1960), 185–264.
Gunning, R., and Rossi, H., Analytic Functions of Several Complex Variables, Prentice-Hall, 1965.
Markuševič, L. A., Approximation by polynomials of continuous functions on Jordan arcs in the space Kn of n complex variables, Sibirsk. Mat. Z. 2 (1961), 237–260, A.M.S. Transl. 57, ser. 2, 144–170.
Royden, H., Algebras of bounded analytic functions on Riemann surfaces, Acta Math. 114 (1965), 113–142.
Rudin, W., Analyticity and the maximum modulus principle, Duke Math. J. 20 (1953), 449–458.
Shapiro, H. S. and Shields, A. A., A sufficient condition for polynomial approximation on an arc in ℂ2, preprint.
Stolzenberg, G., A hull with no analytic structure, J. Math. Mech. 12 (1963), 103–112.
Stolzenberg, G., Uniform approximation on smooth curves, Acta Math. 115 (1966), 195–198.
Wermer, J., Polynomial approximation on an arc in ℂ3, Ann. Math. 62 (1955), 269–270.
Wermer, J., Function rings and Riemann surfaces, Ann. Math. 67 (1958), 45–71.
Wermer, J., Rings of analytic functions, Ann. Math. 67 (1958), 497–516.
Wermer, J., The hull of a curve in ℂn, Ann. Math. 68 (1958), 550–561.
Wermer, J., Banach Algebras, to appear.
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Gamelin, T.W. (1971). Polynomial approximation on thin sets. In: Brooks, R.M. (eds) Symposium on Several Complex Variables, Park City, Utah, 1970. Lecture Notes in Mathematics, vol 184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059278
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DOI: https://doi.org/10.1007/BFb0059278
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