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Displaying 41 – 57 of 57

On the lattice of polynomials with integer coefficients: the covering radius in $L_{p} (0, 1)$

Wojciech Banaszczyk, Artur Lipnicki (2015)

Annales Polonici Mathematici

The paper deals with the approximation by polynomials with integer coefficients in $L_{p} (0, 1)$ , 1 ≤ p ≤ ∞. Let $P_{n, r}$ be the space of polynomials of degree ≤ n which are divisible by the polynomial $x^{r} {(1 - x)}^{r}$ , r ≥ 0, and let $P_{n, r}^{ℤ} \subset P_{n, r}$ be the set of polynomials with integer coefficients. Let $μ (P_{n, r}^{ℤ}; L_{p})$ be the maximal distance of elements of $P_{n, r}$ from $P_{n, r}^{ℤ}$ in $L_{p} (0, 1)$ . We give rather precise quantitative estimates of $μ (P_{n, r}^{ℤ}; L ₂)$ for n ≳ 6r. Then we obtain similar, somewhat less precise, estimates of $μ (P_{n, r}^{ℤ}; L_{p})$ for p ≠ 2. It follows that $μ (P_{n, r}^{ℤ}; L_{p}) ≍ n^{- 2 r - 2 / p}$ as n → ∞. The results partially...

On the maximum modulus of a polynomial and its derivatives.

Dewan, K.K., Mir, Abdullah (2005)

International Journal of Mathematics and Mathematical Sciences

On the maximum modulus of polynomials. II.

Qazi, M.A. (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On the multivariate transfinite diameter

Thomas Bloom, Jean-Paul Calvi (1999)

Annales Polonici Mathematici

We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.

On the operator of Bleimann, Butzer and Hahn.

Ivan, Mircea (1998)

General Mathematics

On the projection norm for a weighted interpolation using Chebyshev polynomials of the second kind.

Smith, Simon J. (2005)

Mathematica Pannonica

On the rate of convergence of Hermite-Fejér polynomials to functions of bounded variation on the zeros of certain Jacobi polynomials

Radwan Al-Jarrah, Abedallah Rababah (1990)

Revista colombiana de matematicas

On the sharpness of an approximation criterion of smoothness for functions on a segment

I. A. Shevchuk (1989)

Banach Center Publications

On the strong summability and approximation of Fourier series

L. Leindler (1979)

Banach Center Publications

On the theorem of Géza Grünwald and Józef Marcinkiewicz

László Szili, Péter Vértesi (2011)

Banach Center Publications

This survey is a tribute to Géza Grünwald and Józef Marcinkiewicz dealing with the so called Grünwald-Marcinkiewicz Theorem.

On weighted $ℒ_{1}$ -approximation by polynomials

Géza Freud (1973)

Studia Mathematica

On Zeros of Polynomials of Best Approximation to Holomorphic and C... Functions.

A.P. Wójcik (1988)

Monatshefte für Mathematik

Optimal Extrapolation of Derivatives.

M.C. Spruill (1987)

Metrika

Optimal Interval Refinement near Singularities.

M. Reimer (1988)

Numerische Mathematik

Optimal Nodes for Interpolation in Hardy Spaces.

Robert Schaback (1982)

Mathematische Zeitschrift

Optimal-order quadratic interpolation in vertices of unstructured triangulations

Josef Dalík (2008)

Applications of Mathematics

We study the problem of Lagrange interpolation of functions of two variables by quadratic polynomials under the condition that nodes of interpolation are vertices of a triangulation. For an extensive class of triangulations we prove that every inner vertex belongs to a local six-tuple of vertices which, used as nodes of interpolation, have the following property: For every smooth function there exists a unique quadratic Lagrange interpolation polynomial and the related local interpolation error...

Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree.

T. Kilgore, J. Prestin, K. Selig (1995)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

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