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Book Review

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Book Information:

Author: J. G. Llavona
Title: Approximation of continuously differentiable functions
Additional book information: North-Holland Mathematics Studies, vol. 130, North-Holland, Amsterdam, 1986, xiv + 241 pp., $48.00. ISBN 0-444-70128-1.

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

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  • 3. R. M. Aron and J. B. Prolla, Polynomial approximation of differentiable functions on Banach spaces, J. Reine Angew Math. 313 (1980), 195-216. MR 552473
  • 4. R. M. Aron and R. M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Funct. Anal. 21 (1976), 7-30. MR 402504
  • 5. S. Bernstein, Leçons sur les propriétés extremales de la meilleure approximation des fonctions analytiques d'une variable réele, Paris, 1926.
  • 6. F. Bombal and J. Llavona, La propiedad de approximación en espacios de funciones differenciables, Rev. R. Acad. Ciencias de Madrid 70 (1976), 337-346. MR 428036
  • 7. M. M. Day, Normed linear spaces, Third ed. Springer-Verlag, New York, 1973. MR 344849
  • 8. J. Lesmes, On the approximation of continuously differentiable functions in Hilbert spaces, Rev. Colombiana Mathemáticas 8 (1974), 217-223. MR 358346
  • 9. J. Llavona, Approximation of differentiable functions, Adv. in Math. Supplementary Studies 4 (1979), 197-221. MR 546807
  • 10. L. Nachbin, Sur les algèbres denses de fonctions différentiables sur une variété, C. R. Acad. Sci. Paris 228 (1949), 1549-1551. MR 30590
  • 11. L. Nachbin, A generalization of Whitney's theorem on ideals of differentiable functions, Proc. Nat. Acad. Sci. U. S. A. 43 (1957), 935-937. MR 90005
  • 12. L. Nachbin and S. Dineen, Entire functions of exponential type bounded on the real axis and Fourier transform of distributions with bounded supports, Israel J. Math. 13 (1972), 321-326. MR 326379
  • 13. J. B. Prolla, On polynomial algebras of continuously differentiable functions, Rend. Accad. Naz. Lincei. 57 (1974), 481-486. MR 423407
  • 14. J. B. Prolla and C. S. Guerreiro, An extension of Nachbin's theorem to differentiable functions on Banach spaces with approximation property, Ark. Math. 14 (1976), 251-258. MR 448077
  • 15. M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-381. MR 1501905
  • 16. K. Sundaresan, Geometry and nonlinear analysis in Banach spaces, Pacific J. Math. 102(1982), 487-498. MR 686565
  • 17. Ch. Vallé Poussin de la, Sur l'approximation des fonctions d'une variable réele et de leurs dérivées par des polynômes et des suites finies de Fourier, Bull. Acad. Sci. Belgique (1908), 193-254.
  • 18. H. Whitney, On ideals of differentiable functions, Amer. J. Math. 70 (1948), 635-658. MR 26238

Review Information:

Reviewer: K. Sundaresan
Journal: Bull. Amer. Math. Soc. 21 (1989), 296-300
DOI: https://doi.org/10.1090/S0273-0979-1989-15834-5
American Mathematical Society