Results 101 to 110 of about 951 (142)
Some of the next articles are maybe not open access.
Mathematical Notes of the Academy of Sciences of the USSR, 1983
Discrete Lebesgue constants \(L_ m(q)\) with \(q\in {\mathbb{N}}\) are studied. An expression for them is \(L_ m(q)=(m+1)/q+\frac{1}{q}\sum^{q- 1}_{\ell =1}| \sin(\pi(m+1)\ell /q)| /\sin(\pi \ell /q).\) Two theorems and a corollary are proved. Theorem 1: For all \(q\geq 2m+2\) the estimates \(\frac{1}{\pi}\log(m+1)+0(1)\leq L_ m(q)\leq \frac{4}{\pi^ 2}\
openaire +1 more source
Discrete Lebesgue constants \(L_ m(q)\) with \(q\in {\mathbb{N}}\) are studied. An expression for them is \(L_ m(q)=(m+1)/q+\frac{1}{q}\sum^{q- 1}_{\ell =1}| \sin(\pi(m+1)\ell /q)| /\sin(\pi \ell /q).\) Two theorems and a corollary are proved. Theorem 1: For all \(q\geq 2m+2\) the estimates \(\frac{1}{\pi}\log(m+1)+0(1)\leq L_ m(q)\leq \frac{4}{\pi^ 2}\
openaire +1 more source
Lebesgue constants for Leja points
IMA Journal of Numerical Analysis, 2008It is shown that for many compact sets in the plane, the Lebesgue constant of interpolation in the first n Leja points cannot grow exponentially in n. This gives a theoretical foundation for the use of Leja points in interpolation.
R. Taylor, V. Totik
openaire +1 more source
The Lebesgue Constants for Regular Hausdorff Methods
Canadian Journal of Mathematics, 1961The 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.
openaire +2 more sources
Weighted Lebesgue Constants: Research Problems 2000-1
Constructive Approximation, 2000The 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.
openaire +1 more source
Evaluation of Lebesgue constant
Approximation Theory and its Applications, 1992Summary: 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.
openaire +2 more sources
Behavior of Lebesgue constants
Mathematical Notes of the Academy of Sciences of the USSR, 1975Upper bounds are obtained for the Lebesgue constants generated by closed, balanced sets in Em with bounded Minkowski upper measure of the boundary.
openaire +1 more source
Lebesgue Constants for Regular Taylor Summabllity
Canadian Mathematical Bulletin, 1965The 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.
openaire +2 more sources
Lebesgue Constants for Cardinal -Spline Interpolation
Canadian Journal of Mathematics, 1977Recently 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
openaire +1 more source
Estimates for lebesgue constants in dimension two
Annali di Matematica Pura ed Applicata, 1990Fourier 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.
openaire +1 more source
Discrete imbedding theorems and Lebesgue constants
Mathematical Notes of the Academy of Sciences of the USSR, 1977The 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.
openaire +1 more source