Shape-preserving Kolmogorov widths of classes of <Emphasis Type="Italic">s</Emphasis>-monotone integrable functions |
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Authors: | V N Konovalov |
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Institution: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev |
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Abstract: | Let s 0 and let
+
s
be the set of functions x defined on a finite interval I and such that, for all collections of s
+ 1 pairwise different points t
0,..., t
s
I, the corresponding divided differences x; t
0,...,t
s
] of order s are nonnegative. Let
+
s
B
p
+
s
B
p, 1 p where B
p is a unit ball in the space L
p, and let
+
s
L
q
+
s
L
q, 1 q . For every s 3 and 1 q p , we determine the exact orders of the shape-preserving Kolmogorov widths IE4 >MATHTYPE >TEX >>{x - y} \right\ L_q , $$]]>, where M
n is the collection of all affine linear manifolds M
n in L
q such that dim M
n n and M
n
+
s
L
q .Translated from Ukrains kyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 901–926, July, 2004. |
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Keywords: | |
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