A counterexample in comonotone approximation in $L^p$ space

Xiang Wu; Song Zhou

Displaying similar documents to “A counterexample in comonotone approximation in $L^{p}$ space”

A note on lacunary approximation on [-1,1]

S. Zhou (1993)

Colloquium Mathematicae

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On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions

S. Zhou (1998)

Colloquium Mathematicae

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We construct a $C^{k}$ piecewise differentiable function that is not $C^{k}$ piecewise analytic and satisfies a Jackson type estimate for approximation by Lagrange interpolating polynomials associated with the extremal points of the Chebyshev polynomials.

A remark on a modified Szász-Mirakjan operator

Guanzhen Zhou, Songping Zhou (1999)

Colloquium Mathematicae

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We prove that, for a sequence of positive numbers δ(n), if $n^{1 / 2} δ (n) \neg \to \infty$ as $n \to \infty$ , to guarantee that the modified Szász-Mirakjan operators $S_{n, δ} (f, x)$ converge to f(x) at every point, f must be identically zero.

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator $W_{k} : = Δ + \frac{k}{x_{n}} \frac{\partial}{\partial x_{n}}$ on $ℝ^{n}$ is proved. In this note there is shown that in the cases $k \neq 0$ , $k \neq 2$ no other transforms of this kind exist and for case $k = 2$ , all such transforms are described.

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and $ℤ_{p}$ the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, $k_{\infty}$ a $ℤ_{p}$ -extension of k, $k_{n}$ the nth layer of $k_{\infty} / k$ , and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ . Iwasawa proved the following well-known theorem about the order $A_{n}$ of $A_{n}$ : Theorem A (Iwasawa). Let $k_{\infty} / k$ be a $ℤ_{p}$ -extension and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ , where $k_{n}$ is the $n$ th layer of $k_{\infty} / k$ . Then there exist integers $λ = λ (k_{\infty} / k) \geq 0$ , $μ = μ (k_{\infty} / k) \geq 0$ , $ν = ν (k_{\infty} / k)$ , and n₀ ≥ 0...

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let $D$ be a nonempty compact subset of a Banach space $X$ and denote by $S (X)$ the family of all nonempty bounded closed convex subsets of $X$ . We endow $S (X)$ with the Hausdorff metric and show that there exists a set $ℱ \subset S (X)$ such that its complement $S (X) ∖ ℱ$ is $σ$ -porous and such that for each $A \in ℱ$ and each $\tilde{x} \in D$ , the set of solutions of the best approximation problem $∥ \tilde{x} - z ∥ \to min$ , $z \in A$ , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

Displaying similar documents to “A counterexample in comonotone approximation in L p space”

A note on lacunary approximation on [-1,1]

On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions

A remark on a modified Szász-Mirakjan operator

On Kelvin type transformation for Weinstein operator

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Best approximations and porous sets

Displaying similar documents to “A counterexample in comonotone approximation in $L^{p}$ space”