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Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here.
V.E. Maiorov On various widths of the class H p r H^{r}_{p} in the space L q L_{q} Izv. Akad. Nauk SSSR Ser. Mat. 42
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V.N Temlyakov, Approximation of periodic functions of several variables with bounded mixed difference, Mat. Sb., 133
1982
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C. Schütt, Entropy numbers of diagonal operators between symmetric Banach spaces, J. Approx. Theory
1984
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Ding Dung, Approximation of multivariate functions by means of harmonic analysis, Hab. Dissertation
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M.A. Lifshits and B.S. Tsirelson, Small deviations of Gaussian fields, Teor. Probab. Appl
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R.F. Bass, Probability estimates for multiparameter Brownian processes, Ann. Probab
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E.D. Gluskin, Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces, Mat. Sb., 136
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V.N. Temlyakov, On estimates of ϵ \epsilon -entropy and widths of classes of functions with bounded mixed derivative or difference, Dokl. Akad. Nauk SSSR
1988
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V.N. Temlyakov, Approximation of functions with bounded mixed derivative, Trudy MIAN, 178
1989
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V.N. Temlyakov, Estimates of the asymptotic characteristics of classes of functions with bounded mixed derivative or difference, Trudy Matem. Inst. Steklov
1990
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V.N. Temlyakov, Estimates of Best Bilinear Approximations of Functions and Approximation Numbers of Integral Operators, Mat. Zametki, 51
1992
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J. Kuelbs and W.V. Li, Metric entropy and the small ball problem for Gaussian measures, J. Functional Analysis
1993
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D. Offin and K. Oskolkov, A note on orthonormal polynomial bases and wavelets, Constructive Approx. 9
1993
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V.N. Temlyakov, Bilinear Approximation and Related Questions, Trudy Mat. Inst. Steklov, 194
1993
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E.S. Belinsky, Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative, J. Approx. Theory
1998
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R.A. DeVore, Nonlinear approximation Acta Numerica
1998
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V.N. Temlyakov, On two problems in the multivariate approximation, East J. Approx
1998
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V.N. Temlyakov, Greedy Algorithms with Regards to Multivariate Systems with Special Structure, Constructive Approximation, 16
2000
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B.S. Kashin and V.N. Temlyakov, The volume estimates and their applications, East J. Approx
2003
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H. Triebel, Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration, European Mathematical Society, Germany, 2010
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V.N. Temlyakov, Approximation of periodic functions
1993
Cited alongside, same era.
B. S. Kashin and V. N. Temlyakov, On best m m -terms approximations and the entropy of sets in the space L 1 L^{1} , Mat. Zametki, 56
1994
Cited alongside, same era.
M. Talagrand, The small ball problem for the Brownian sheet, Ann. Probab
1994
Cited alongside, same era.
B.S. Kashin and V.N. Temlyakov, Estimate of approximate characteristics for classes of functions with bounded mixed derivative, Math. Notes
1995
Cited alongside, same era.
V.N. Temlyakov, An inequality for trigonometric polynomials and its application for estimating the entropy numbers, J. Complexity
1995
Cited alongside, same era.
V.N. Temlyakov, Some inequalities for multivariate Haar polynomials, East J. Approx
1995
Cited alongside, same era.
S.A. Smolyak, The ϵ \epsilon -entropy of the classes E s α k ( B ) E^{\alpha k}_{s}(B) and W s α ( B ) W^{\alpha}_{s}(B) in the metric L 2 L_{2} , Dokl. Akad. Nauk SSSR
Cited in the paper.
2010
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V.N. Temlyakov, Greedy approximation, Cambridge University Press, 2011
2011
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V.N. Temlyakov, An inequality for the entropy numbers and its application, J. Approximation Theory, 173
2013
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V.N. Temlyakov, Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness, Matem. Sb. 206
2014
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2015
Later among the works it cites.