Absolute widths of some embeddings

Timur Oikhberg

doi:10.1006/jath.1995.1036

Absolute widths of some embeddings

Research output: Contribution to journal › Article › peer-review

Abstract

The absolute widths of the natural identity operator Iⁿ_pq, mapping lⁿ_p to lⁿ_q, for 1 ≤ q ≤ p ≤ ∞, are considered. The main result of this workis the following:THEOREM 1. If 1 ≤ q ≤ p ≤ ∞, 0 ≤ m ≤ n, d^a_m(Iⁿ_pq) = (n - m)^1/q-1/q, whered^a_m(u) stands for the absolute width of the operator u.

Original language	English (US)
Pages (from-to)	120-126
Number of pages	7
Journal	Journal of Approximation Theory
Volume	81
Issue number	1
DOIs	https://doi.org/10.1006/jath.1995.1036
State	Published - Apr 1995
Externally published	Yes

ASJC Scopus subject areas

Analysis
Numerical Analysis
Mathematics(all)
Applied Mathematics

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10.1006/jath.1995.1036

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abstract = "The absolute widths of the natural identity operator Inpq, mapping lnp to lnq, for 1 ≤ q ≤ p ≤ ∞, are considered. The main result of this workis the following:THEOREM 1. If 1 ≤ q ≤ p ≤ ∞, 0 ≤ m ≤ n, dam(Inpq) = (n - m)1/q-1/q, wheredam(u) stands for the absolute width of the operator u.",

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Absolute widths of some embeddings

Abstract

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