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Boundedness of Lebesgue Constants and Interpolating Faber Bases

Наукові вісті Національного технічного університету України "Київський політехнічний інститут", 2017
Background. We investigate the relationship between the boundedness of Lebesgue constants for the Lagrange polynomial interpolation on a compact subset of \[\mathbb R\] and the existence of a Faber basis in the space of continuous functions on this ...
Viktoriia V. Bilet, Oleksiy A. Dovgoshey, Jürgen Prestin   +2 more
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Integrals of subharmonic functions and their differences with weight over small sets on a ray

Математичні Студії, 2020
Let $E$ be a measurable subset in a segment $[0,r]$ in the positive part of the real axis in the complex plane, and $U=u-v$ be the difference of subharmonic functions $u\not\equiv -\infty$ and $v\not\equiv -\infty$ on the complex plane.
B.N. Khabibullin
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Lebesgue Constants for Jacobi Expansions [PDF]

Proceedings of the American Mathematical Society, 1983
Sharp estimates are given for the Lebesgue constants | | | s n | | | p = sup {
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Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials

Journal of Applied Mathematics, 2013
Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher
Hee Sun Jung, Ryozi Sakai
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L^p-Solution to the Random Linear Delay Differential Equation with a Stochastic Forcing Term

Mathematics, 2020
This paper aims at extending a previous contribution dealing with the random autonomous-homogeneous linear differential equation with discrete delay τ > 0 , by adding a random forcing term f ( t ) that varies with time: x ′ ( t ) =
Juan Carlos Cortés, Marc Jornet
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On a two-dimensional analogue of the Lebesgue function for Fourier-Chebyshov sums [PDF]

E3S Web of Conferences
This article considers the problem of approximating a function of two variables f(x,y) by Fourier sums over Chebyshev polynomials orthogonal on a discrete grid.
Rustanov A.R., Shikhshinatova M.M.
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The τ-fixed point property for nonexpansive mappings

Abstract and Applied Analysis, 1998
Let X be a Banach space and τ a topology on X. We say that X has the τ-fixed point property (τ-FPP) if every nonexpansive mapping T defined from a bounded convex τ-sequentially compact subset C of X into C has a fixed point.
Tomás Domínguez Benavides, jesús García Falset, Maria A. Japón Pineda   +2 more
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A Blaschke–Lebesgue theorem for the Cheeger constant

Communications in Contemporary Mathematics, 2023
In this paper, we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux polygon together with an explicit upper bound for the inradius of the optimal domain.
Antoine Henrot, Ilaria Lucardesi
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Lebesgue constants for Cantor sets. Numerical results

Journal of Numerical Analysis and Approximation Theory
We analyze numerically the form of Lebesgue functions and the values of Lebesgue constants in polynomial interpolation for three types of Cantor sets.
Alexander Goncharov, Yiğit Görgülü, Yaman Paksoy   +2 more
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Spectral approximations of strongly degenerate elliptic differential operators

Karpatsʹkì Matematičnì Publìkacìï, 2019
We establish analytical estimates of spectral approximations errors for strongly degenerate elliptic differential operators in the Lebesgue space $L_q(\Omega)$ on a bounded domain $\Omega$.
M.I. Dmytryshyn, O.V. Lopushansky
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