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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF
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. Errett Bishop, A generalization of the Stone-Weierstrass theorem, Pacific J. Math. 11 (1961), 777–783. MR 0133676
  • 3. R. Creighton Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95–104. MR 0105611
  • 4. R. B. Burckel, Characterizations of 𝐶(𝑋) among its subalgebras, Marcel Dekker, Inc., New York, 1972. Lecture Notes in Pure and Applied Mathematics, Vol. 6. MR 0442687
  • 5. Alain Goullet de Rugy, Espaces de fonctions pondérables, Israel J. Math. 12 (1972), 147–160 (French, with English summary). MR 0324386
  • 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. Leopoldo Nachbin, Weighted approximation over topological spaces and the Bernstein problem over finite dimensional vector spaces, Topology 3 (1964), no. suppl. 1, 125–130. MR 0161077
  • 8. 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 0176353
  • 9. 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
  • 10. Jo ao B. Prolla, Weighted spaces of vector-valued continuous functions, Ann. Mat. Pura Appl. (4) 89 (1971), 145–157. MR 0308771
  • 11. G. E. Šilov, On rings of functions with uniform convergence, Ukrain. Mat. Žurnal 3 (1951), 404–411 (Russian). MR 0054178
  • 12. M. H. Stone, The generalized Weierstrass approximation theorem, Math. Mag. 21 (1948), 167–184, 237–254. MR 0027121

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