Exact values of relative widths of classes of differentialbe functions

Subbotin, Yu. N.; Telyakovskiĭ, S. A.

doi:10.1007/bf02675588

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Cited by 11 publications

(7 citation statements)

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“…Subbotin and Telyakovskii in [12], [13], [14], Tikhomirov in [18], Babenko in [1], [2], [3], Konovalov in [6], [7], [8], Shevaldin in [17] etc. obtained many results in this field.…”

Section: Introductionmentioning

confidence: 99%

Relative widths of function classes of L 2(T) defined by a linear differential operator in L q (T)

Xiao

2011

Anal Math

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“…Subbotin and Telyakovskii in [12], [13], [14], Tikhomirov in [18], Babenko in [1], [2], [3], Konovalov in [6], [7], [8], Shevaldin in [17] etc. obtained many results in this field.…”

Section: Introductionmentioning

confidence: 99%

Relative widths of function classes of L 2(T) defined by a linear differential operator in L q (T)

Xiao

2011

Anal Math

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“…The second problem was studied by Babenko [2] for r = 1, 2 and p = q = 1, by Subbotin and Telyakovskii [11,12] for r ∈ Z + =: {1, 2, . .…”

Section: Introductionmentioning

confidence: 99%

Relative average widths of Sobolev spaces in L 2(ℝ d )

Liu

Xiao

2008

Anal Math

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A b s t r a c t . In this paper, in order to consider the problems of relative width on R d , we proposed definitions of relative average width which combine the ideas of the relative width and the average width. We established the smallest number M which make the following equality2 ) is the Riesz potential or Bessel potential of the unit ball in L 2 (R k ) and the notations Kσ(·, ·, L2(R d )) and dσ(·, L2(R d )) denote respectively the relative average width in the sense of Kolmogorov and the average width in the sense of Kolmogorov in their given order. In 2001, Subbotin and Telyakovskii got similar results on the relative width of Kolmogorov type. We also proved that, U(W β 2 ) ∩ B(L2(R d ))L2(R d )) = dσ(U (W α 2 ), L2(R d )), where 0 < β < α.

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“…Nevertheless, some estimates of relative shapepreserving -widths have been obtained in papers [3][4][5]. Estimates of relative (not necessary shape-preserving) widths have been obtained in works [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%