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Book Review

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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.

References [Enhancements On Off] (What's this?)

  • 1. 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
  • 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 Bernšteĭn-Nachbin approximation problem, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 1, vii, 193–206 (English, with French summary). 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

Review Information:

Reviewer: W. H. Summers
Journal: Bull. Amer. Math. Soc. 1 (1979), 420-424
DOI: https://doi.org/10.1090/S0273-0979-1979-14624-X
American Mathematical Society