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Book Review
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Book Information
Author(s):
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
References:
- 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
Additional Information:
Reviewer(s):
W. H.
Summers
Review Information:
Journal:
Bull. Amer. Math. Soc.
1
(1979),
420-424.
DOI:
10.1090/S0273-0979-1979-14624-X
PII:
S 0273-0979(1979)14624-X
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