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For n ∈ ℕ, L > 0, and p ≥ 1 let $κ_{p} (n, L)$ be the largest possible value of k for which there is a polynomial P ≢ 0 of the form $P (x) = \sum_{j = 0}^{n} a_{j} x^{j}$ , $| a_{0} | \geq L (\sum_{j = 1}^{n} | a_{j} {|^{p})}^{1 / p}$ , $a_{j} \in ℂ$ , such that ${(x - 1)}^{k}$ divides P(x). For n ∈ ℕ, L > 0, and q ≥ 1 let $μ_{q} (n, L)$ be the smallest value of k for which there is a polynomial Q of degree k with complex coefficients such that $| Q (0) | > 1 / L (\sum_{j = 1}^{n} {| Q (j) |}^{q})^{1 / q}$ . We find the size of $κ_{p} (n, L)$ and $μ_{q} (n, L)$ for all n ∈ ℕ, L > 0, and 1 ≤ p,q ≤ ∞. The result about $μ_{\infty} (n, L)$ is due to Coppersmith and Rivlin, but our proof is completely different and much shorter even in that special...

Corrected Fourier series and its application to function approximation.

Zhang, Qing-Hua, Chen, Shuiming, Qu, Yuanyuan (2005)

International Journal of Mathematics and Mathematical Sciences

Correction to the paper: Continuous dependence of the local strong unicity constant on domain (Aequationes Math. 46 (1993), 229-242).

Charles B. Dunham, Chang Z. Zhu (1996)

Aequationes mathematicae

Correction to “Walsh equiconvergence for best $l_{2}$ approximates” Studia Math.. 77 (1984), 523-528

A. Sharma, Z. Ziegler (1987)

Studia Mathematica

Corrigendum on "Semigroup-theoretical proofs of the central limit theorem and other theorems of analysis.

J. Goldstein (1976)

Semigroup forum

Corrigendum to "The Existence and Unicity of Best Approximations".

E.W. Cheney, D.E. Wulbert (1970)

Mathematica Scandinavica

Corrigendum to the paper "Pointwise convergence for expansions in surface harmonics of arbitrary dimension".

E.L. Roetman (1976)

Journal für die reine und angewandte Mathematik

Counterexamples in optimal quadrature.

Arthur G. Werschulz (1985)

Aequationes mathematicae

C-Polynomials for Rational Approximation to the Exponential Function.

S.P. Norsett (1975/1976)

Numerische Mathematik

Criteria for membership of the Besov spaces BS pq.

Finbarr Holland, David Walsh (1989)

Mathematische Annalen

Cubature Formulae which are Exact on Spaces P, Intermediate Between Pk and Qk.

A. Guessab (1986)

Numerische Mathematik

Cubic splines with minimal norm

Jiří Kobza (2002)

Applications of Mathematics

Natural cubic interpolatory splines are known to have a minimal $L_{2}$ -norm of its second derivative on the $C^{2}$ (or $W_{2}^{2})$ class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite $C^{1}$ splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed....

Curriculum vita of Prof. Vasil Atanasov Popov

Ivanov, Kamen, Petrushev, Pencho (2002)

Serdica Mathematical Journal

Our primary goal in this preamble is to highlight the best of Vasil Popov’s mathematical achievements and ideas. V. Popov showed his extraordinary talent for mathematics in his early papers in the (typically Bulgarian) area of approximation in the Hausdorff metric. His results in this area are very well presented in the monograph of his advisor Bl. Sendov, “Hausdorff Approximation”.

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