Bulletin of the American Mathematical Society

MathSciNet review: 1567135
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Book Information:

Author: João B. Prolla
Title: Approximation of vector valued functions
Additional book information: Mathematics Studies 25, North-Holland Publishing Company, Amsterdam, New York, Oxford, 1977, xiii + 219 pp., $22.50.

S. Bernstein, La problème de l’approximation des fonctions continues sur tout l’axe réel et l’une de ses applications, Bull. Soc. Math. France 52 (1924), 399–410 (French). MR 1504852

Errett Bishop, A generalization of the Stone-Weierstrass theorem, Pacific J. Math. 11 (1961), 777–783. MR 133676

R. Creighton Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95–104. MR 105611

R. B. Burckel, Characterizations of $C(X)$ among its subalgebras, Lecture Notes in Pure and Applied Mathematics, Vol. 6, Marcel Dekker, Inc., New York, 1972. MR 0442687

Alain Goullet de Rugy, Espaces de fonctions pondérables, Israel J. Math. 12 (1972), 147–160 (French, with English summary). MR 324386, DOI 10.1007/BF02764659

S. Machado and J. B. Prolla, The general complex case of the Bernšteĭn-Nachbin approximation problem, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 1, vii, 193–206 (English, with French summary). MR 500921

Leopoldo Nachbin, Weighted approximation over topological spaces and the Bernstein problem over finite dimensional vector spaces, Topology 3 (1964), no. suppl, suppl. 1, 125–130. MR 161077, DOI 10.1016/0040-9383(64)90011-4

Leopoldo Nachbin, Weighted approximation for algebras and modules of continuous functions: Real and self-adjoint complex cases, Ann. of Math. (2) 81 (1965), 289–302. MR 176353, DOI 10.2307/1970617

Leopoldo Nachbin, Elements of approximation theory, Van Nostrand Mathematical Studies, No. 14, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0217483

João B. Prolla, Weighted spaces of vector-valued continuous functions, Ann. Mat. Pura Appl. (4) 89 (1971), 145–157. MR 308771, DOI 10.1007/BF02414945

G. E. Šilov, On rings of functions with uniform convergence, Ukrain. Mat. Žurnal 3 (1951), 404–411 (Russian). MR 0054178

M. H. Stone, The generalized Weierstrass approximation theorem, Math. Mag. 21 (1948), 167–184, 237–254. MR 27121, DOI 10.2307/3029750

1.

S. Bernstein, Le problème de l'approximation des fonctions continues sur tout l'axe réel et l'une de ses applications, Bull. Soc. Math. France 52 (1924), 399-410. MR 1504852

2.

E. Bishop, A generalization of the Stone-Weierstrass Theorem, Pacific J. Math. 11 (1961), 777-783. MR 133676

3.

R. C. Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95-104. MR 105611

4.

R. B. Burckel, Characterizations of C (X) among its subalgebras, Lecture Notes in Pure and Appl. Math., vol. 6, Marcel Dekker, New York, 1972. MR 442687

5.

A. Goullet de Rugy, Espaces de fonctions pondérables, Israel J. Math. 12 (1972), 147-160. MR 324386

6.

S. Machado and J. B. Prolla, The general complex case of the Bernstein-Nachbin approximation problem, Ann. Inst. Fourier (Grenoble) (to appear). MR 500921

7.

L. Nachbin, Weighted approximation over topological spaces and the Bernstein problem over finite dimensional vector spaces, Topology 3, suppl. 1 (1964), 125-130. MR 161077

8.

L. Nachbin, Weighted approximation for algebras and modules of continuous functions: real and self-adjoint complex cases, Ann. of Math. (2) 81 (1965), 289-302. MR 176353

9.

L. Nachbin, Elements of approximation theory, Van Nostrand Math. Studies, No. 14, Van Nostrand, Princeton, N. J., 1967. MR 217483

10.

J. B. Prolla, Weighted spaces of vector-valued continuous functions, Ann. Mat. Pura Appl. 89 (1971), 145-158. MR 308771

11.

G. E. Šilov, On rings of functions with uniform convergence, Ukrain. Mat. Z. 3 (1951), 404-411. MR 54178

12.

M. H. Stone, The generalized Weierstrass approximation theorem, Math. Magazine 21 (1948), 167-184; 237-254. MR 27121