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Estimate of approximate characteristics for classes of functions with bounded mixed derivative. (English. Russian original) Zbl 0878.46023

Math. Notes 58, No. 6, 1340-1342 (1995); translation from Mat. Zametki 58, No. 6, 922-925 (1995).
The authors supplement an earlier paper of theirs [Math. Notes 56, No. 5, 1137-1157 (1994; Zbl 0836.41008)] by establishing lower bounds for the \(\varepsilon\)-entropy numbers and Kolmogorov widths of additional classes of spaces of functions of several variables having bounded mixed derivatives.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy

Citations:

Zbl 0836.41008
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References:

[1] B. S. Kashin and V. N. Temlyakov,Mat. Zametki [Math. Notes],56, No. 5, 57–86 (1994).
[2] É. S. Belinskii, ”Asymptotic characteristics of function classes with restrictions on the mixed derivative (mixed difference),” in:Studies in the Theory of Functions of Several Real Variables [in Russian], Yaroslavl State University, Yaroslavl (1990), pp. 22–37.
[3] V. N. Temlyakov,Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],301, No. 2, 288–291 (1988).
[4] V. N. Temlyakov, ”Estimates of asymptotic characteristics for classes of functions with bounded mixed derivative or difference,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],189 138–168 (1989).
[5] A. Pietsch,Operator Ideals, Deutsch. Verlag Wissensch., Berlin (1978); English transl.: North-Holland, Amsterdam (1980).
[6] Din’ Zung,Approximation of Smooth Functions of Several Variables by Means of Harmonic Analysis, D. Sc. Thesis, Moscow State University, Moscow (1985). · Zbl 0605.41033
[7] V. N. Temlyakov,Approximation of Periodic Functions, Nova Science Publishers (1993). · Zbl 0899.41001
[8] V. N. Temlyakov, ”Approximation of functions with bounded mixed derivative,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],178, 1–121, (1986). · Zbl 0668.41024
[9] G. G. Lorentz,Bull. Amer. Math. Soc.,72, 903–937 (1966). · Zbl 0158.13603
[10] G. Pisier,The Volume of Convex Bodies and Banach Space Geometry, Cambridge University Press, Cambridge (1989). · Zbl 0698.46008
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