Bounds from below and diameters of classes of periodic functions with a bounded fractional derivative
type: Item
instance of: scholarly article
title: Bounds from below and diameters of classes of periodic functions with a bounded fractional derivative
zbMATH Open document ID: 0799.42003
DOI: 10.1007/BF01208331
published in: Mathematical Notes
publication date: 1994-07-13T00:00:00Z
review text: Using the notations of the paper the main result reads as follows: Let \(\alpha \in {\mathfrak R}\), \(r \geq 1\) and \(m \leq C \cdot (r + 1)\). Then \[ d_{2m -1} (W_ \infty^{r, \alpha})_ \infty = d_{2m}(W_ \infty^{r,\alpha})_ \infty = d_{2m - 1} (W_ 1^{r,\alpha})_ 1 = {4 \over \pi m^ r} M_{r,\alpha}. \]
reviewed by: László Leindler
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 567885
zbMATH Keywords: diameters
zbMATH Keywords: widths
zbMATH Keywords: classes of periodic functions
zbMATH Keywords: fractional derivative
author: Valerii T. Shevaldin
MaRDI profile type: Publication
cites work: Q3726518
cites work: Q5671098
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cites work: Q5540873
cites work: DIAMETERS OF SETS IN FUNCTION SPACES AND THE THEORY OF BEST APPROXIMATIONS
cites work: Q5602378
cites work: Functions of exponential type
full work available at URL: https://doi.org/10.1007/bf01208331
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description: scientific article; zbMATH DE number 567885