Literature Cited
D. J. Newman and H. S. Shapiro, “Jackson's theorem in higher dimensions,” in: International Series of Numerical Mathematics, Vol. 5, On Approximation Theory, Birkhauser Verlag, Basel and Stuttgart (1964), pp. 208–219.
V. A. Yudin, “The multidimensional Jackson theorem,” Mat. Zametki,20, No. 3, 439–444 (1976).
M. I. Ganzburg, “Theorems of Jackson and Bernshtein in Rm,” Usp. Mat. Nauk,34, No. 1, 225–226 (1979).
M. I. Ganzburg, “A multidimensional limit theorem of the theory of best polynomial approximations,” Dokl. Akad. Nauk SSSR,242, No. 1, 17–20 (1978).
E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton (1971).
N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).
G. Polya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Princeton Univ. Press, Princeton (1951).
L. Talenti, “Elliptic equations and rearrangements,” Ann. Scoula Norm. Super Pisa,3, No. 4, 697–718 (1977).
T. G. Genchev, “Entire functions of exponential type with polynomial growth on R nx ,” J. Math. Anal. Appl.,60, No. 1, 103–119 (1977).
S. M. Nikol'skii, Approximation of Functions of Several Variables and Embedding Theorems [in Russian], Nauka, Moscow (1977).
S. N. Bernshtein, “On the best approximation of continuous functions on the whole real axis by means of entire functions of given degree. I–V,” in: Collected Works [in Russian], Vol. 2, Izd. Akad. Nauk SSSR, Moscow (1954), pp. 371–395.
A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).
Yu. A. Brudnyi, “The multidimensional analog of the Whitney theorem,” Mat. Sb.,82, No. 2, 175–191 (1970).
V. I. Burenkov, “On the additivity of the classes W (r)p (ω),” Tr. Mat. Inst. Akad. Nauk SSSR,89, 31–55 (1967).
P. P. Korovkin, “On an asymptotic property of positive methods of summation of Fourier series and on the best approximation of functions of the class Z2 by positive linear polynomial operators,” Usp. Mat. Nauk,13, No. 6, 99–103 (1958).
L. Danszer, B. Grünbaum, and V. Klee, The Helley Theorem and Its Applications [Russian translation], Mir, Moscow (1968).
G. G. Lorentz, “Lower bounds for the degree of approximation,” Trans. Am. Math. Soc.,97, 25–34 (1960).
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All-Union Scientific-Research Institute for Mechanization of Labor in Ferrous Metallurgy, Dnepropetrovsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 22, No. 2, pp. 74–83, March–April, 1981.
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Ganzburg, M.I. Multidimensional Jackson theorems. Sib Math J 22, 223–231 (1981). https://doi.org/10.1007/BF00968419
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DOI: https://doi.org/10.1007/BF00968419