Abstract
The purpose of this note is to give a survey of some recent results on uniqueness of best multivariate approximation in C and L1 -norms.
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References
B. Brosowski, C-Guerreiro, Conditions for the Uniqueness of best Generalized Rational Chebyshev Approximation to Differentiable and Analytic Functions, J. Approx. Th. 42 (1984) 149–17–3.
L. Collatz, Approximation von Funktionen bei einer and bei, mehreven Veranderlichen, Zeit. Angew. Math. Mech., 36 (1956), 198 – 211
H. Ehrlich, K.Zeller, Cebysev-Polynome in mehreren Veranderlichen, Math, Zeit.-93 (1966), 142 – 143
Fromm, L1- approximation to Zero, Math Zeit 151 (1976), 31 – 33
A.L.Garkavi, Dimensionality of polyhedra of best approximation for differentiable functions, zv - Akad.Nauk SSSR, ser. math., 23 (1959), 93 – 114
A.Kroó, Some theorems on unicity of multivariate L1-app-roximation, Acta Math.. Acad. Sci. Hungar., 40 (1982), 179 – 189
A.Kroó, On the unicity of best L1 - approximation by polynomials of several variables, Acta Math, Hung. 42 (1.983)5 309–318.
A.Kroó, On Chebyshev subspaces in the space of multivariate differentiable functions, Trans. Amer. Math.Soc., to appear..
A.Kroó, on the unicity of best Chebyshev approximation of differentiable functions, Acta Sci. Math.. Szeged, 47 (1984), to appear
A.Kroó, On an L1-approximation problem, Proc Amer Math Soc., to appear..
A-Kroó, A genaral approach to the study of Chebyshev subspaces in L1- approximation of continuous functions, to appear.
A.Pinkus, Unicity subspaces in L1 -approximation, J. Approx. Th. to appear.
T`J. RivIin,B.S.Shapiro,Some uniqueness probIems in approximation theory, Comm. Pure Appl-Math., 131 (1960)., 3,51–47
H.S..Shapiro, Topics in Approximation Theory, Lecture Notes in Math. 187, Springer Verlag (Berlin-Heidelberg-New York 1971 )
H.Strauss, Best L1 -approximation, J -Approx. Th. 41 (1984) 297 – 308
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© 1985 Birkhäuser Verlag Basel
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Kroó, A. (1985). Some uniqueness problems in best Chebyshev and mean multivariate approximation. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory III. International Series of Numerical Mathematics, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9321-3_25
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DOI: https://doi.org/10.1007/978-3-0348-9321-3_25
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