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作者：Mirek, Mariusz; Stein, Elias M.; Trojan, Bartosz
作者单位：Institute for Advanced Study - USA; University of Wroclaw; Princeton University; Wroclaw University of Science & Technology
摘要：We prove l(p)(Z(d)) bounds for p is an element of(1,infinity) of r-variations r is an element of(2,infinity) for discrete averaging operators and truncated singular integrals of Radon type. We shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts.
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作者：Blumenthal, Alex; Young, Lai-Sang
作者单位：New York University
摘要：We consider C-2 Frechet differentiable mappings of Banach spaces leaving invariant compactly supported Borel probability measures, and study the relation between entropy and volume growth for a natural notion of volume defined on finite dimensional subspaces. SRB measures are characterized as exactly those measures for which entropy is equal to volume growth on unstable manifolds, equivalently the sum of positive Lyapunov exponents of the map. In addition to numerous difficulties incurred by o...
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作者：Guo, Yan; Kim, Chanwoo; Tonon, Daniela; Trescases, Ariane
作者单位：Brown University; University of Wisconsin System; University of Wisconsin Madison; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite Paris Saclay
摘要：A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical solutions away from the grazing set for all boundary conditi...
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作者：Fresan, Javier
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：At the end of the 1970s, Gross and Deligne conjectured that periods of geometric Hodge structures with multiplication by an abelian number field are products of values of the gamma function at rational arguments, with exponents determined by the Hodge decomposition. We prove an alternating variant of this conjecture for smooth projective varieties acted upon by an automorphism of finite order, thus improving previous results of Maillot and Rossler. The proof relies on a product formula for per...
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作者：Miao, Shuang; Yu, Pin
作者单位：University of Michigan System; University of Michigan; Tsinghua University
摘要：The paper is devoted to the study of shock formation of the 3-dimensional quasilinear wave equation -(1 + 3G ''(0)(partial derivative(t)phi)(2))partial derivative(2)(t)phi + Delta phi = 0, where is a non-zero constant. We will exhibit a family of smooth initial data and show that the foliation of the incoming characteristic hypersurfaces collapses. Similar to 1-dimensional conservational laws, we refer this specific type breakdown of smooth solutions as shock formation. Since satisfies the cla...
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作者：Le, Nam Q.; Savin, Ovidiu
作者单位：Indiana University System; Indiana University Bloomington; Columbia University
摘要：We obtain estimates up to the boundary for solutions to degenerate Monge-AmpSre equations of the type det D(2)u = f in Omega, f similar to dist(alpha)(., partial derivative Omega) near partial derivative Omega, alpha > 0. As a consequence we obtain global estimates up to the boundary for the eigenfunctions of the Monge-AmpSre operator on smooth, bounded, uniformly convex domains in R-n.
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作者：Radu, Nicolas
作者单位：Universite Catholique Louvain
摘要：Let T be a locally finite tree all of whose vertices have valency at least 6. We classify, up to isomorphism, the closed subgroups of acting 2-transitively on the set of ends of T and whose local action at each vertex contains the alternating group. The outcome of the classification for a fixed tree T is a countable family of groups, all containing two remarkable subgroups: a simple subgroup of index and (the semiregular analog of) the universal locally alternating group of Burger-Mozes (with ...
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作者：Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
作者单位：Lund University; California Institute of Technology; California Institute of Technology; University of New Mexico
摘要：We consider Chebyshev polynomials, T-n(z), for infinite, compact sets e subset of R (that is, the monic polynomials minimizing the sup-norm,parallel to T-n parallel to(e), on ). We resolve a 45+ year old conjecture of Widom that for finite gap subsets of R , his conjectured asymptotics (which we call Szego-Widom asymptotics) holds. We also prove the first upper bounds of the form parallel to T-n parallel to(e) <= QC(e)(n) (where C (e) is the logarithmic capacity of e) for a class of e's with a...
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作者：Baraud, Y.; Birge, L.; Sart, M.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：The aim of this paper is to present a new estimation procedure that can be applied in various statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density estimation, they asymptotically coincide with the celebrated maximum likelihood estimators at least when the statistical model is regular enough and contains the true density to estimate. For very general models of densities, including non-compact ones, these es...
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作者：Bertola, Marco; Korotkin, Dmitry; Norton, Chaya
作者单位：Concordia University - Canada; Universite de Montreal; International School for Advanced Studies (SISSA)
摘要：We study the symplectic geometry of the space of linear differential equations with holomorphic coefficients of the form on Riemann surfaces of genus g. This space coincides with the moduli space of projective connections which is an affine bundle modelled on the cotangent bundle . We show that for several choices of the origin, or base, holomorphic projective connection (such as Bergman, Wirtinger or Schottky) the canonical Poisson structure on induces the Goldman bracket on the monodromy cha...
