On nonlinear -widths

Authors:
Dinh Dung and Vu Quoc Thanh

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2757-2765

MSC (1991):
Primary 41A46, 41A25, 41A63, 42A10

DOI:
https://doi.org/10.1090/S0002-9939-96-03337-0

MathSciNet review:
1327007

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Abstract | References | Similar Articles | Additional Information

Abstract: For characterization of best nonlinear approximation, DeVore,

Howard, and Micchelli have recently suggested the nonlinear -width of a subset in a normed linear space . We proved by a topological method that for and the well-known Aleksandrov -width in a Banach space the following inequalities hold: . Let be the unit ball of Besov space , of multivariate periodic functions. Then for approximation in , with some restriction on and , we established the asymptotic degree of these -widths: .

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Additional Information

**Dinh Dung**

Affiliation:
Institute of Information Technology, Nghia Do, Tu Liem, Hanoi 10000, Vietnam

Email:
ddung@math-ioit.ac.vn

**Vu Quoc Thanh**

Affiliation:
Institute of Information Technology, Nghia Do, Tu Liem, Hanoi 10000, Vietnam

DOI:
https://doi.org/10.1090/S0002-9939-96-03337-0

Keywords:
Nonlinear approximation,
$n$-widths,
Besov space

Received by editor(s):
April 8, 1992

Received by editor(s) in revised form:
March 8, 1995

Additional Notes:
This work was supported by Project 1.5.5 of the Vietnamese National Program for Researches in Natural Sciences.

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1996
American Mathematical Society