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81
Jacobi approximations in nonuniformly Jacobiweighted Sobolev spaces
 JOURNAL OF APPROXIMATION THEORY
, 2004
"... Jacobi approximations in nonuniformly Jacobiweighted Sobolev spaces are investigated. Some results on orthogonal projections and interpolations are established. Explicit expressions describingthe dependence of approximation results on the parameters of Jacobi polynomials are given. These results s ..."
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Cited by 26 (14 self)
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Jacobi approximations in nonuniformly Jacobiweighted Sobolev spaces are investigated. Some results on orthogonal projections and interpolations are established. Explicit expressions describingthe dependence of approximation results on the parameters of Jacobi polynomials are given. These results
OPTIMAL ERROR ESTIMATES IN JACOBIWEIGHTED SOBOLEV SPACES FOR POLYNOMIAL APPROXIMATIONS ON THE TRIANGLE
"... Abstract. Spectral approximations on the triangle by orthogonal polynomials are studied in this paper. Optimal error estimates in weighted seminorms for both the L2 − and H1 0 −orthogonal polynomial projections are established by using the generalized Koornwinder polynomials and the properties of t ..."
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Cited by 8 (4 self)
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Abstract. Spectral approximations on the triangle by orthogonal polynomials are studied in this paper. Optimal error estimates in weighted seminorms for both the L2 − and H1 0 −orthogonal polynomial projections are established by using the generalized Koornwinder polynomials and the properties
APPROXIMATION THEORY FOR THE PVERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS IN THE FRAMEWROK OF JACOBIWEIGHTED BESOV SPACES Part I: Approximabilities of singular functions
"... This paper is the first in a series devoted to the approximation theory of the pversion of the finite element method in three dimensions. In this paper, we introduce the Jacobiweighted Besov and Sobolev spaces in the threedimensional setting and analyze the approximability of functions in the fra ..."
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Cited by 12 (1 self)
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This paper is the first in a series devoted to the approximation theory of the pversion of the finite element method in three dimensions. In this paper, we introduce the Jacobiweighted Besov and Sobolev spaces in the threedimensional setting and analyze the approximability of functions
Refined Sobolev inequalities in Lorentz spaces
, 2009
"... We establish refined Sobolev inequalities between the Lorentz spaces and homogeneous Besov spaces. The sharpness of these inequalities is illustrated on several examples, in particular based on nonuniformly oscillating functions known as chirps. These results are also used to derive refined Hardy i ..."
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Cited by 2 (0 self)
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We establish refined Sobolev inequalities between the Lorentz spaces and homogeneous Besov spaces. The sharpness of these inequalities is illustrated on several examples, in particular based on nonuniformly oscillating functions known as chirps. These results are also used to derive refined Hardy
Selection in Functional ANOVA Models with Nonuniform Data
"... Functional ANOVA models have emerged as a class of structured models usefull to capture nonlinear relations in the data, while still providing insight in the model and dealing appropriately with the curse of dimensionality. The general principle behind functional ANOVA models is to approximate the f ..."
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, or where they are taken from the uniform distribution over the multidimensional unit interval. In this case the Sobolev embedding traditionally used in nonparametric statistics is optimal in the sense that it leads to mutually uncorrelated components. Besides being useful for interpretation, this latter
Nonuniform dependence on initial data for the CH equation on the line
 Differential Integral Equations
"... Abstract. For s> 3/2 two sequences of CH solutions living in a bounded set of the Sobolev space Hs(R) are constructed, whose distance at the initial time is converging to zero while at any later time is bounded below by a positive constant. This implies that the solution map of the CH equation is ..."
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Cited by 5 (1 self)
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Abstract. For s> 3/2 two sequences of CH solutions living in a bounded set of the Sobolev space Hs(R) are constructed, whose distance at the initial time is converging to zero while at any later time is bounded below by a positive constant. This implies that the solution map of the CH equation
Sobolev orthogonal polynomials; weight; weighted Sobolev spaces on curves
, 805
"... Abstract. In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To h ..."
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Abstract. In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights
Direct and inverse approximation theorems for the pversion of the finite element method in the framework of weighted Besov spaces. I. Approximability of functions in the weighted Besov spaces
 SIAM J. Numer. Anal
"... Abstract. This is the first of a series devoted to the approximation theory of the pversion of the finite element method in two dimensions in the framework of the Jacobiweighted Besov spaces, which provides the pversion with a solid mathematical foundation. In this paper, we establish a mathemati ..."
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Cited by 8 (4 self)
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mathematical framework of the Jacobiweighted Besov and Sobolev spaces and analyze the approximability of the functions in the framework of these spaces, particularly, singular functions of rγtype and rγ logν rtype. These spaces and the corresponding approximation properties are of fundamental importance
Supraconvergence of a NonUniform Discretisation for an Elliptic ThirdKind BoundaryValue Problem with Mixed Derivatives
"... Abstract. The thirdkind boundaryvalue problem for an elliptic equation of second order with variable coefficients and mixed as well as firstorder terms on a domain that is the union of rectangles is approximated by a linear finite element method with firstorder accurate quadrature. The scheme i ..."
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is equivalent to a standard finite difference method. Although the discretisation is in general only firstorder consistent, supraconvergence, i.e. convergence of higher order, is shown to take place even on nonuniform grids. Local error estimates of optimal order min(s, 3/2) in the H1(Ω)norm can be derived
A DegreeIndependent Sobolev Extension Operator
, 2004
"... We consider a domain Ω ⊂ R n and the Sobolev spaces W k,p of functions with k derivatives in L p. It is well known that extension operators from W k,p (Ω) to W k,p (R n) exist only under some assumptions on the geometry of Ω. In the case that Ω has Lipschitz boundary, Calderón showed that for each ..."
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operator on locally uniform domains. This is a much larger class of domains that includes examples with highly nonrectifiable boundaries. Jones also proved that these are the sharp class of domains for extension of Sobolev spaces in R 2. The operators constructed by Jones are degree
Results 1  10
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81