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Transactions of the American Mathematical Society

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On Chebyshev subspaces in the space of multivariate differentiable functions


Author: András Kroó
Journal: Trans. Amer. Math. Soc. 287 (1985), 839-852
MSC: Primary 41A50; Secondary 41A10
DOI: https://doi.org/10.1090/S0002-9947-1985-0768745-8
MathSciNet review: 768745
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Abstract: In the present paper we give a characterization of Chebyshev sub-spaces in the space of (real or complex) continuously-differentiable functions of two variables. We also discuss various applications of the characterization theorem.


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  • [1] B. Brosowski, Tschebysheffsche Approximationen an differenzierbare Funktionen, Z. Angew. Math. Mech. 46 (1966), T39-T40. MR 0227681 (37:3265)
  • [2] B. Brosowski and H. L. Loeb, Zur Eindeutigkeit der rationalen Tschebyscheff-Approximationen an stetig differenzierbare Funktionen, Numer. Math. 10 (1967), 51-55. MR 0216219 (35:7054)
  • [3] B. Brosowski and Y. Stoer, Zur rationalen Tschebyscheff-Approximation differenzierbare und analytischer Funktionen, Numer. Math. 12 (1968), 57-65. MR 0240531 (39:1878)
  • [4] L. Collatz, Approximation von Funktionen bei einer und bei mehreren Veränderlichen, Z. Angew. Math. Mech. 36 (1956), 198-211. MR 0083198 (18:677d)
  • [5] A. L. Garkavi, Dimensionality of polyhedra of best approximation for differentiable functions, Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 93-114. (Russian) MR 0104957 (21:3706)
  • [6] A. Haar, Die Minkowskische Geometrie und die Annäherung an stetige Funktionen, Math. Ann. 78 (1918), 294-311. MR 1511900
  • [7] A. N. Kolmogorov, A remark on the polynomials of P. L. Čebyšev deviating the least from a given function, Uspekhi Mat. Nauk 3 (1948), 216-221. (Russian) MR 0025609 (10:35b)
  • [8] A. Kroó, On the unicity of best Chebyshev approximation of differentiable functions, Acta Sci. Math. (Szeged) 47 (1984) (to appear). MR 783312 (86g:41046)
  • [9] J. C. Mairhuber, On Haar's theorem concerning Chebyshev approximation problems having unique solution, Proc. Amer. Math. Soc. 7 (1956), 609-615. MR 0079672 (18:125g)
  • [10] T. J. Rivlin and H. S. Shapiro, Some uniqueness problems in approximation theory, Comm. Pure Appl. Math. 13 (1960), 35-47. MR 0123127 (23:A458)
  • [11] H. S. Shapiro, Topics in Approximation theory, Lecture Notes in Math., Vol. 187, Springer-Verlag, Berlin, Heidelberg and New York, 1971. MR 0437981 (55:10902)
  • [12] I. Singer, Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, Berlin, Heidelberg and New York, 1970. MR 0270044 (42:4937)
  • [13] V. I. Smirnov and N. A. Lebedev, Functions of a complex variable, constructive theory, Iliffe, London, 1968. MR 0229803 (37:5369)
  • [14] K. Zeller and H. Ehrlich, Čebyšev-Polynome in mehreren Veränderlichen, Math. Z. 93 (1966), 142-143. MR 0198069 (33:6228)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0768745-8
Article copyright: © Copyright 1985 American Mathematical Society

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