Results 81 to 90 of about 1,753 (100)

The Lebesgue Constants for Regular Hausdorff Methods

Canadian Journal of Mathematics, 1961
The unboundedness of the sequence of Lebesgue constants (norms), at a point, of certain transforms implies, as is well known, that there exist (i) a continuous function whose transform fails to converge to the function at the point in question (the du Bois-Reymond singularity), and (ii) another such function whose transform, while converging everywhere
Lorch, L., Newman, D. J.
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Weighted Lebesgue Constants: Research Problems 2000-1

Constructive Approximation, 2000
The paper poses the following research problem: Characterize those weight functions \(w:J\to [0,\infty[\), for which there exists a triangular array \(\Gamma=(x_{j,k})_{0\leq j\leq k}\) of interpolation points such that \[ \sup_{x \in J}w(x) \sum^n_{j=1} \bigl|\ell_{j,n}(x) \bigr|w^{-1} (x_{j,n})= O(\log n),\;n\to\infty, \] where \((\ell_{j,n})^n_{j=1}\
Lubinsky, D. S., Szabados, J.
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Evaluation of Lebesgue constant

Approximation Theory and its Applications, 1992
Summary: The Lebesgue constant associated with interpolation at nodes \(U\) is evaluated in this note. The main result is an improvement on the estimate obtained by Brutman.
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Behavior of Lebesgue constants

Mathematical Notes of the Academy of Sciences of the USSR, 1975
Upper bounds are obtained for the Lebesgue constants generated by closed, balanced sets in Em with bounded Minkowski upper measure of the boundary.
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Lebesgue Constants for Regular Taylor Summabllity

Canadian Mathematical Bulletin, 1965
The nth Taylor mean of order r of a sequence {sn} is given by1.1where1.2Cowling [l] has shown that this method is regular if and only if 0 ≦ r < 1. Since r = 0 corresponds to ordinary convergence, it will be assumed here that 0 < r < 1.
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Lebesgue Constants for Cardinal -Spline Interpolation

Canadian Journal of Mathematics, 1977
Recently the theory of cardinal polynomial spline interpolation was extended to cardinals -splines [3]. Letbe a polynomial with only real zeros. Denote the set of zeros by . If is the associated differential operator, the null-space
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Estimates for lebesgue constants in dimension two

Annali di Matematica Pura ed Applicata, 1990
Fourier series of integrable functions fail to converge in the mean. The divergence is measured by the \(L^ 1\)-norms of the Dirichlet kernel; they are called Lebesgue constants and they provide positive summability results for certain classes of functions [cf. \textit{D. I. Cartwright} and \textit{P. M. Soardi}, J.
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Discrete imbedding theorems and Lebesgue constants

Mathematical Notes of the Academy of Sciences of the USSR, 1977
The order of growth of the Lebesgue constant for a “hyperbolic cross” is found: $$L_R = \smallint _{T^2 } \left| {\sum\nolimits_{0< \left| {v_1 v_2 } \right| \leqslant R^2 } {e^{2\pi ivx} } } \right|dx\begin{array}{*{20}c} \smile \\ \frown \\ \end{array} R^{1/_2 } , R \to \infty $$ . Estimates are obtained by applying a discrete imbedding theorem.
Yudin, A. A., Yudin, V. A.
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Uniform Lebesgue Constants of Local Spline Approximation

Proceedings of the Steklov Institute of Mathematics, 2018
The new splines with equidistant knots were proposed in a previous article of the author of this article. The splines define a linear (noninterpolation) method \(S\) of approximation of functions on the real line or on its interval. The uniform Lebesgue constants (the norms of linear operators from \(C\) to \(C\)) of these splines are studied in this ...
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Lebesgue Constants for Some Interpolating L-Splines

Proceedings of the Steklov Institute of Mathematics, 2018
The author considers interpolating splines that are bounded on the real axis, have equidistant knots, and correspond to linear differential operators of the form \(\mathcal{L}_3 := D(D^2+\alpha^2)\), where \(\alpha > 0\). Exact values for the uniform Lebesgue constant of such splines are found and compared to the Lebesgue constants of other \(\mathcal ...
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