Search Results

You are looking at 21 - 30 of 44 items for :

  • "best approximation" x
  • Mathematics and Statistics x
  • Refine by Access: All Content x
Clear All

Реэюме  

Получены точные неравенства типа Джексона-Стечкина для ос-редненных с весом модулей непрерывности m-го (m ∈ ℕ) порядка. Для классов функций, определенных при помоши мажорант и укаэанных осредненных величин, вычислены точные эначения раэличных n-поперечников при выполнении определенных ограничений на мажоранты.

Restricted access

LÖFSTRÖM, J., Best approximation in L p (w) by algebraic polynomials, Studia Sci. Math. Hungar. 20 (1985), 375-394. MR 88e :41023 Best approximation in L p (w) by algebraic polynomials Studia Sci

Restricted access

Abstract  

The best rate of approximation of functions on the sphere by spherical polynomials is majorized by recently introduced moduli of smoothness. The treatment applies to a wide class of Banach spaces of functions.

Restricted access

We consider the weighted Hermite-Fejér interpolation process based on Jacobi nodes for classes of locally continuous functions defined by another Jacobi weight. Necessary and sufficient conditions for the weighted norm boundedness and for the convergence, as well as error estimates of the approximation, are given.

Restricted access

In the paper we construct such second order linear recursive sequences G and H of rational integers that with their terms |a -G n+1 /H n| < 1/ (\sqrtvD H 2 n) holds for every positive integer n, where a denotes a real quadratic algebraic integer of discriminant D. An approximating sequence of the form G n+1 /H n is also given for a  if it is only a real quadratic algebraic number (not an algebraic integer), but in this case the approximating constant is not the best.

Restricted access

Abstract  

We introduce a new class of sequences called NBVS to generalize GBVS, essentially extending monotonicity from “one sided” to “two sided”, while some important classical results keep true.

Restricted access
The norm estimation problem for Fourier operators acting from L w p (
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
) to L υ q (
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
) where 1 < pq < ∞ was investigated. These results has been generalized to the two-dimensional case and applied to obtain generalizations of the Bernstein inequality for trigonometric polynomials of one and two variables. Also, the rates of convergence of Cesaro and Abel-Poisson means of functions fL w p (
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
) has been estimated in the case p = q and υw . The generalized Bernstein inequality applied to estimate the order of best trigonometric approximation of the derivative of functions fL w p (
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
) in the space L υ q (
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
).
Restricted access

Abstract  

We obtain estimates of approximations by angle in Hardy and L p spaces in terms of double Fourier-Vilenkin coefficients. Analogous results are also established for best approximations in the one-dimensional case.

Restricted access

We present applications of Hermite polynomials in signal analysis. Among other result, we give a characterization of the so-called time-frequency window functions in terms of the Hermite--Fourier coefficients, a Bernstein-type theorem for the best approximations of window functions by Hermite-functions, time-frequency approximations. Some analogues for Hankel-transforms will also be considered.

Restricted access