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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On $ n$-widths of certain functional classes defined by linear differential operators


Author: Y. Makovoz
Journal: Proc. Amer. Math. Soc. 89 (1983), 109-112
MSC: Primary 41A46
DOI: https://doi.org/10.1090/S0002-9939-1983-0706520-4
MathSciNet review: 706520
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Abstract: Let $ A = {D^r} + \sum\nolimits_{k = 0}^{r - 1} {{a_k}(t){D^k}} $, $ {a_k} \in {C^k}$, be a differential operator and let $ {W_p}(A)$ be the class of functions $ x(t)$ for which $ \left\Vert {Ax} \right\Vert \leqslant 1$ in $ {L_p}[0,1]$. We prove that the asymptotic behavior of the Kolmogorov widths $ {d_n}({W_p}(A),{L_q})$, $ 1 \leqslant p$, $ q \leqslant \infty $, when $ n \to \infty $ does not depend on $ {a_k}$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0706520-4
Keywords: $ n$-widths, differential operators
Article copyright: © Copyright 1983 American Mathematical Society

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