Approximation theory and imbedding problems

Authors

  • A.B. Németh Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat21-12
Abstract views: 340

Abstract

Not available.

Downloads

Download data is not yet available.

References

Boltjanskiĭ, V. G., Mappings of compacta into Euclidean spaces. (Russian) Izv. Akad. Nauk SSSR. Ser. Mat. 23 1959 871-892, MR0117707.

Boltjanskiĭ, V. G.; Ryškov, S. S.; Šaškin, Ju. A. On k-regular imbeddings and on applications to theory of function approximation. Uspehi Mat. Nauk 15 1960 no. 6 (96), 125-132, (Russian) MR0125567

Borsuk, K., On the k-independent subsets of the Euclidean space and of the Hilbert space. Bull. Acad. Polon. Sci. Cl. III. 5 (1957), 351-356, XXIX., MR0088710.

Curtis, Philip C., Jr., n-parameter families and best approximation. Pacific J. Math. 9 1959 1013-1027, MR0108670, https://doi.org/10.2140/pjm.1959.9.1013 DOI: https://doi.org/10.2140/pjm.1959.9.1013

Dunham, Charles B., Unisolvence on multidimensional spaces. Canad. Math. Bull. 11 1968 469-474, MR0235362, https://doi.org/10.4153/cmb-1968-056-6 DOI: https://doi.org/10.4153/CMB-1968-056-6

Haar, A., Die Minkowskische Geometrie and die annäherung an stetige Funktionen, Math. Ann. 78, 294-311, 1918, https://doi.org/10.1007/bf01457106 DOI: https://doi.org/10.1007/BF01457106

Hewitt, E,. Stromberg, K., Real and abstract analysis. A modern treatment of the theory of functions of a real variable. Springer-Verlag, New York 1965 vii+476 pp., MR0188387.

Kiefer, J., Wolfowitz, J., On a theorem of Hoel and Levine on extrapolation designs. Ann. Math. Statist. 36 1965 1627-1655, MR0185769, https://doi.org/10.1214/aoms/1177699793 DOI: https://doi.org/10.1214/aoms/1177699793

Lutts, John A., Topological spaces which admit unisolvent systems. Trans. Amer. Math. Soc. 111 1964 440-448, MR0163286, https://doi.org/10.1090/s0002-9947-1964-0163286-x DOI: https://doi.org/10.1090/S0002-9947-1964-0163286-X

Mairhuber, John C., On Haar's theorem concerning Chebychev approximation problems having unique solutions. Proc. Amer. Math. Soc. 7 (1956), 609-615, MR0079672, https://doi.org/10.1090/s0002-9939-1956-0079672-3 DOI: https://doi.org/10.1090/S0002-9939-1956-0079672-3

Németh, A. B., Transformations of the Chebyshev systems. Mathematica (Cluj) 8 (31) 1966 315-333, MR0213787.

Németh, A. B., Homeomorphic projections of k-independent sets and Chebyshev subspaces of finite dimensional Chebyshev spaces. Mathematica (Cluj) 9 (32) 1967 325-333,MR0235367.

Németh, A. B., About an imbedding conjecture for k-independent sets. Fund. Math. 67 1970 203-207, MR0261576, https://doi.org/10.4064/fm-67-2-203-207 DOI: https://doi.org/10.4064/fm-67-2-203-207

Phelps, Robert R., Lectures on Choquet's theorem. D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London 1966 v+130 pp., MR0193470.

MR0033516 Reviewed Pontryagin, L. S. Osnovy Kombinatornoĭ Topologii. [Foundations of Combinatorial Topology] OGIZ, Moscow-Leningrad,] 1947. 143 pp. (Russian)

Rubinšteĭn, G. Š., On a method of investigation of convex sets. Dokl. Akad. Nauk SSSR (N.S.) 102 (1955), 451-454, (Russian) MR0071793.

Ryškov, S. S., On k-regular imbeddings. Dokl. Akad. Nauk SSSR 127 1959 272-273, (Russian) MR0111004.

Schoenberg, I. J.; Yang, C. T., On the unicity of solutions of problems of best approximation. Ann. Mat. Pura Appl. (4) 54 1961 1-12, MR0141927, https://doi.org/10.1007/bf02415339 DOI: https://doi.org/10.1007/BF02415339

Sieklucki, K., Topological properties of sets admitting the Tschebycheff systems. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 1958 603-606, MR0100192.

Šaškin, Ju. A., Korovkin systems in spaces of continuous functions. Izv. Akad. Nauk SSSR Ser. Mat. 26 1962 495-512, (Russian) MR0147905.

Šaškin, Ju. A., Topological properties of sets connected with approximation theory. Izv. Akad. Nauk SSSR Ser. Mat. 29 1965 1085-1094, (Russian) MR0203700.

Šaškin, Ju. A., Interpolation families of functions and imbeddings of sets in Euclidean and projective spaces. Dokl. Akad. Nauk SSSR 174 1967 1030-1032, (Russian) MR0216487.

Šaškin, Ju. A., - (Russian)

Volkov, V. I., Some properties of Čebyšev systems. Kalinin. Gos. Ped. Inst. Uč. Zap. 26 1958 41-48, (Russian) MR0131102.

Yang, C. T. On the non-orientable closed surfaces in euclidean spaces. Canad. J. Math. 14 1962 660-668, MR0142118, https://doi.org/10.4153/cjm-1962-056-1 DOI: https://doi.org/10.4153/CJM-1962-056-1

Downloads

Published

1973-02-01

How to Cite

Németh, A. (1973). Approximation theory and imbedding problems. Rev. Anal. Numér. Théorie Approximation, 2, 61–67. https://doi.org/10.33993/jnaat21-12

Issue

Vol. 2 (1973)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.