Results 81 to 90 of about 2,532 (218)
Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs
Communications on Pure and Applied Mathematics, Volume 79, Issue 4, Page 1012-1072, April 2026.Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
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Bounds for Lebesgue Functions for Freud Weights
Journal of Approximation Theory, 1994 The role of the Lebesgue function of Lagrange interpolation is well understood for arrays of interpolation points that lie in a fixed finite interval, for example, \([-1,1]\). The size of the Lebesgue function governs the pointwise convergence of the Lagrange interpolation process. It was G.
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Macroscopic Market Making Games
Mathematical Finance, Volume 36, Issue 2, Page 352-373, April 2026.ABSTRACT Building on the macroscopic market making framework as a control problem, this paper investigates its extension to stochastic games. In the context of price competition, each agent is benchmarked against the best quote offered by the others. We begin with the linear case.
Ivan Guo, Shijia Jin
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Seeking a constructive proof of a theorem of Khrushchev
Concrete OperatorsWe discuss a classical theorem of Khrushchev, which establishes that any set of positive Lebesgue measure on the circle supports a function with a continuous Cauchy transform.
Malman Bartosz
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The Lebesgue Function and Lebesgue Constant of Lagrange Interpolation for Erdoős Weights
Journal of Approximation Theory, 1998 An Erdős weight is of the form \(W(x)=\exp(-Q(x))\) where \(Q(x)\) is even and grows faster than any polynomial at infinity. For a given weight \(W\) and a given set of nodes \(\{\xi_{1n},\ldots,\xi_{nn}\}\subset{\mathbb R}\), the Lebesgue function is \(\Lambda_n(x)=W(x)W_n(x)\) where \(W_n\) is the Lagrange interpolating polynomial of \(W^{-1}\) for ...
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Order Routing and Market Quality: Who Benefits From Internalization?
Mathematical Finance, Volume 36, Issue 2, Page 397-421, April 2026.ABSTRACT Does retail order internalization benefit (via price improvement) or harm (via reduced liquidity) retail traders? To answer this question, we compare two market designs that differ in their mode of liquidity provision: In the setting capturing retail order internalization, liquidity is provided by market makers (wholesalers) competing for the ...
Umut Çeti̇n, Albina Danilova
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Some bounds related to the 2‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 2, April 2026.Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
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APPROXIMATIVE PROPERTIES OF FOURIER-MEIXNER SUMS
Проблемы анализа, 2018 We consider the problem of approximation of discrete functions f = f(x) defined on the set Ω_δ = {0, δ, 2δ, . . .}, where δ =1/N, N > 0, using the Fourier sums in the modified Meixner polynomials M_(α;n,N)(x) = M(α;n)(Nx) (n = 0, 1, . . .), which for α >
Gadzhimirzaev R. M.
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Young's functional with Lebesgue-Stieltjes integrals
, 2011 For non-decreasing real functions $f$ and $g$, we consider the functional $ T(f,g ; I,J)=\int_{I} f(x)\di g(x) + \int_J g(x)\di f(x)$, where $I$ and $J$ are intervals with $J\subseteq I$. In particular case with $I=[a,t]$, $J=[a,s]$, $s\leq t$ and $g(x)=x$, this reduces to the expression in classical Young's inequality.
Merkle, Milan +4 more
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Discrepancy of arithmetic progressions in boxes and convex bodies
Mathematika, Volume 72, Issue 2, April 2026.Abstract The combinatorial discrepancy of arithmetic progressions inside [N]:={1,…,N}$[N]:= \lbrace 1, \ldots, N\rbrace$ is the smallest integer D$D$ for which [N]$[N]$ can be colored with two colors so that any arithmetic progression in [N]$[N]$ contains at most D$D$ more elements from one color class than the other.
Lily Li, Aleksandar Nikolov
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