This article is cited in 1 scientific paper (total in 1 paper)
On an estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions
E. A. Sevast'yanov
This paper establishes best possible conditions, on the degree of approximation of functions $f(x_1,…,x_m)$ in $L_p([0,1]^m)$ ($0<p\leqslant\infty$) by rational functions, that guarantee that the function $f$ has a $p$th mean differential of order $\lambda>0$ everywhere except on a set of zero Hausdorff ($m-1+\alpha$) measure ($0<\alpha\leqslant1$).
Bibliography: 11 titles.
PDF file (2067 kB)
Mathematics of the USSR-Izvestiya, 1986, 26:2, 347–369
MSC: 41A20, 26B05
E. A. Sevast'yanov, “On an estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions”, Izv. Akad. Nauk SSSR Ser. Mat., 49:2 (1985), 369–392; Math. USSR-Izv., 26:2 (1986), 347–369
Citation in format AMSBIB
\paper On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
Komarov M.A., “Distribution of the Logarithmic Derivative of a Rational Function on the Line”, Acta Math. Hung.
|Number of views:|