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Book Review
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Book Information
Author(s):
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:
- 1.
- T. Abuabara, A version of the Paley-Wiener-Schwartz theorem in infinite dimensions, Advances in Holomorphy, North-Holland Math. Studies 34 (1979), 1-29. MR 520652
- 2.
- R. M. Aron, C. Herves, and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983), 189-203. MR 707203
- 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
Additional Information:
Reviewer(s):
K.
Sundaresan
Review Information:
Journal:
Bull. Amer. Math. Soc.
21
(1989),
296-300.
DOI:
10.1090/S0273-0979-1989-15834-5
PII:
S 0273-0979(1989)15834-5
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