Results 51 to 60 of about 4,705,780 (288)
Optimal stencils in Sobolev spaces [PDF]
IMA Journal of Numerical Analysis, 2017 This paper proves that the approximation of pointwise derivatives of order $s$ of functions in Sobolev space $W_2^m(\R^d)$ by linear combinations of function values cannot have a convergence rate better than $m-s-d/2$, no matter how many nodes are used for approximation and where they are placed.
Davydov, Oleg, Schaback, Robert
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Sobolev spaces and the Cayley transform [PDF]
Proceedings of the American Mathematical Society, 2005 The generalised Cayley transform C \mathcal {C} from an Iwasawa N N -group into the corresponding real unit sphere S \mathbb {S} induces isomorphisms between suitable Sobolev spaces H α ( S
ASTENGO, FRANCESCA, DI BLASIO B.
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Weighted Variable Sobolev Spaces and Capacity
Journal of Function Spaces and Applications, 2012 We define weighted variable Sobolev capacity and discuss properties of capacity in the space 𝑊1,𝑝(⋅)(ℝ𝑛,𝑤). We investigate the role of capacity in the pointwise definition of functions in this space if the Hardy-Littlewood maximal operator is bounded on ...
Ismail Aydin
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Multivariate box spline wavelets in higher-dimensional Sobolev spaces
Journal of Inequalities and Applications, 2018 We construct wavelets and derive a density condition of MRA in a higher-dimensional Sobolev space. We give necessary and sufficient conditions for orthonormality of wavelets in Hs(Rd) $H^{s}(\mathbb {R}^{d})$.
Raj Kumar, Manish Chauhan
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G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE [PDF]
, 2014 We introduce a new notion of G-expectation-weighted Sobolev spaces, or in short, G-Sobolev spaces, and prove that a backward SDEs driven by G-Brownian motion are in fact path dependent PDEs in the corresponding Sobolev spaces under G-norms.
Peng, Shige, Song, Yongsheng
core
A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces
Journal of Inequalities and Applications, 2016 In recent years, nonhomogeneous wavelet frames have attracted some mathematicians’ interest. This paper investigates such problems in a Sobolev space setting. A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces pairs is obtained.
Jian-Ping Zhang, Yun-Zhang Li
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A note on the Malliavin–Sobolev spaces [PDF]
Statistics & Probability Letters, 2016 In this paper, we provide a strong formulation of the stochastic G{ }teaux differentiability in order to study the sharpness of a new characterization, introduced in [6], of the Malliavin-Sobolev spaces. We also give a new internal structure of these spaces in the sense of sets inclusion.
Imkeller, Peter +3 more
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First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, EarlyView.Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
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Duality properties of metric Sobolev spaces and capacity
Mathematics in Engineering, 2021 We study the properties of the dual Sobolev space $H^{-1,q}(\mathbb{X})= \big(H^{1,p}(\mathbb{X})\big)'$ on a complete extended metric-topological measure space $\mathbb{X}=(X,\tau,\rm{d},\rm{m})$ for $p\in (1,\infty)$.
Luigi Ambrosio, Giuseppe Savaré
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The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space [PDF]
, 2007 It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant.
Benguria, Rafael D. +2 more
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