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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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  • 2. R. M. Aron, C. Hervés, and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983), no. 2, 189–204. MR 707203, 10.1016/0022-1236(83)90081-2
  • 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, 10.1515/crll.1980.313.195
  • 4. Richard M. Aron and M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Functional Analysis 21 (1976), no. 1, 7–30. MR 0402504
  • 5. S. Bernstein, Leçons sur les propriétés extremales de la meilleure approximation des fonctions analytiques d'une variable réele, Paris, 1926.
  • 6. F. Bombal Gordón, The Arens product in locally convex algebras, Rev. Real Acad. Ci. Exact. Fís. Natur. Madrid 70 (1976), no. 2, 337–346 (Spanish). MR 0428036
  • 7. Mahlon M. Day, Normed linear spaces, 3rd ed., Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21. MR 0344849
  • 8. Jaime Lesmes, On the approximation of continuously differentiable functions in Hilbert spaces, Rev. Colombiana Mat. 8 (1974), 217–223. MR 0358346
  • 9. José G. Llavona, Approximations of differentiable functions, Studies in analysis, Adv. in Math. Suppl. Stud., vol. 4, Academic Press, New York-London, 1979, pp. 197–221. MR 546807
  • 10. Leopoldo Nachbin, Sur les algèbres denses de fonctions différentiables sur une variété, C. R. Acad. Sci. Paris 228 (1949), 1549–1551 (French). MR 0030590
  • 11. Leopoldo Nachbin, A generalization of Whitney’s theorem on ideals of differentiable functions, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 935–937. MR 0090005
  • 12. Leopoldo Nachbin and Seán Dineen, Entire functions of exponential type bounded on the real axis and Fourier transforms of distributions with bounded supports, Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces (Jerusalem, 1972), 1972, pp. 321–326 (1973). MR 0326379
  • 13. Jo ao B. Prolla, On polynomial algebras of continuously differentiable functions, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 57 (1974), no. 6, 481–486 (1975) (English, with Italian summary). MR 0423407
  • 14. Jo ao B. Prolla and Claudia S. Guerreiro, An extension of Nachbin’s theorem to differentiable functions on Banach spaces with the approximation property, Ark. Mat. 14 (1976), no. 2, 251–258. MR 0448077
  • 15. M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375–481. MR 1501905, 10.1090/S0002-9947-1937-1501905-7
  • 16. Kondagunta Sundaresan, Geometry and nonlinear analysis in Banach spaces, Pacific J. Math. 102 (1982), no. 2, 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. Hassler Whitney, On ideals of differentiable functions, Amer. J. Math. 70 (1948), 635–658. MR 0026238

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