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希尔伯特(Hilbert,David，1862～1943)（图）
希尔伯特 德国 数学
2015/1/21
希尔伯特，D.(Hilbert,David，1862～1943)德国数学。
他于1900年8月8日在巴黎第二届国际数学家大会上，提出了新世纪数学家应当努力解决的23个数学问题，被认为是20世纪数学的制高点，对这些问题的研究有力推动了20世纪数学的发展，在世界上产生了深远的影响。希尔伯特领导的数学学派是19世纪末20世纪初数学界的一面旗帜，希尔伯特被称为“数学界的无冕之王”。
给出了非伸展映像的概念，并且在Hilbert空间中证明了非伸展映像与非扩张映像不动点的弱收敛定理. 所得结果改进和拓展了Osilike和Isiogugu 以及其他作者的相关结果.
We prove that the analogue for the Hilbert transform of a classical weighted inequality by Fefferman and Stein for the Hardy Littlewood maximal operator does not hold. This is a sequel to paper arXiv:...
Local properties of Hilbert spaces of Dirichlet series
Local properties Hilbert spaces Dirichlet series
2010/11/19
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This ex...
Mass equidistribution of Hilbert modular eigenforms
Mass equidistribution Hilbert modular eigenforms
2010/11/11
Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show th...
Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces
Characterizing projective spaces deformations Hilbert schemes of K3 surfaces
2010/11/11
We seek to characterize homology classes of Lagrangian projective spaces embedded in irreducible holomorphic-symplectic manifolds, up to the action of the monodromy group. This paper addresses the ca...
Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space
Nonlinear Control Systems Kernel Hilbert Space
2010/11/19
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the ...
Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation
Hilbert schemes of points locally planar curve Severi strata of its versal deformation
2010/11/30
Let C be a locally planar curve. Its versal deformation admits a stratification by the genera of the fibres. The strata are singular; we show that their multiplicities at the central
point are determ...
Hilbert space compression under direct limits and certain group extensions
Hilbert space compression direct limits certain group extensions
2010/12/3
We find bounds on the Hilbert space compression of the limit of a directed metric system of groups. We also give estimates on the Hilbert space compression of group extensions of a group H by a a word...
On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles
cohomology groups of local systems Hilbert modular varieties Higgs bundles
2010/12/3
Let X be a Hilbert modular variety and V a non-trivial local system over X. In this paper we study Deligne-Saito’s mixed Hodge structure (MHS) on the cohomology groups Hk(X, V) using the method of Hig...
The Standard Conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces
Standard Conjectures holomorphic symplectic varieties deformation Hilbert schemes of K3 surfaces
2010/11/29
We prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky’s theory of hyperholomorphic shea...
Inexact Newton regularization methods in Hilbert scales
Inexact Newton regularization methods Hilbert scales
2010/12/9
We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.