ASYMPTOTIC PROPERTIES OF KOLMOGOROV WIDTHS
نویسندگان
چکیده
منابع مشابه
Asymptotic properties of Kolmogorov widths
The first problem studied in the paper is relations between the Kolmogorov n-width of a compact and its projections. The second problem is: to what extent the width can change if we enlarge the space. 2000 Mathematics Subject Classification: 46B20, 41A46, 41A65
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If L is a bounded linear operator mapping the Banach space X into the Banach space Y and K is a compact set in X, then the Kolmogorov widths of the image L(K) do not exceed those of K multiplied by the norm of L. We extend this result from linear maps to holomorphic mappings u from X to Y in the following sense: when the n widths of K are O(n−r) for some r > 1, then those of u(K) are O(n−s) for...
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We study the dependence of the Kolmogorov widths of a compact set on the ambient Banach space.
متن کاملBASIC PROPERTIES OF LINEAR RELATIVE n-WIDTHS
The paper examines the basic properties of linear relative widths as well as the different ways of finding their estimates. AMS Subject Classification: 41A35, 41A29
متن کاملComparison theorems of Kolmogorov type and exact values of n-widths on Hardy-Sobolev classes
Let Sβ := {z ∈ C : |Imz| < β} be a strip in complex plane. H̃r ∞,β denotes those 2π-periodic, real-valued functions on R which are analytic in the strip Sβ and satisfy the condition |f (r)(z)| ≤ 1, z ∈ Sβ . Osipenko and Wilderotter obtained the exact values of the Kolmogorov, linear, Gel′fand, and information n-widths of H̃r ∞,β in L∞[0, 2π], r = 0, 1, 2, . . ., and 2n-widths of H̃r ∞,β in Lq [0, ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2010
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972710000043