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101.
The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give applications to Riesz inequalities. 相似文献
102.
Gregory E. Fasshauer 《Advances in Computational Mathematics》1999,10(1):81-96
We show how conditionally negative definite functions on spheres coupled with strictly completely monotone functions (or functions
whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained
have the advantage over the strictly positive definite functions studied in [17] that closed form representations (as opposed
to series expansions) are readily available. Furthermore, our functions include the historically significant spherical multiquadrics.
Numerical results are also presented.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
103.
Received January 5, 1997 / Revised version received November 19, 1997 Published online November 24, 1998 相似文献
104.
Received February 10, 1997 / Revised version received June 6, 1998 Published online October 9, 1998 相似文献
105.
Received June 4, 1996 / Revised version received November 19, 1997
Published online November 24, 1998 相似文献
106.
Winfried Sickel Frauke Sprengel 《Journal of Computational Analysis and Applications》1999,1(3):263-288
We investigate the order of convergence of periodic interpolation on sparse grids (blending interpolation) in the framework of tensor products of Nikol'skij–Besov spaces. To this end, we make use of the uniformity of the considered tensor norms and provide a unified approach to error estimates for the interpolation of univariate periodic functions from Nikol'skij–Besov spaces. 相似文献
107.
Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible
flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point
out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals
are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory
property; It turns out there is a connection between our examples and Micchelli’s work. 相似文献
108.
Consider a kind of Hermit interpolation for scattered data of 3D by trivariate polynomial natural spline,such that the objective energy functional (with natural boundary conditions) is minimal.By the s... 相似文献
109.
Support-type properties of generalized convex functions 总被引:1,自引:0,他引:1
Szymon W?sowicz 《Journal of Mathematical Analysis and Applications》2010,365(1):415-747
Chebyshev systems induce in a natural way a concept of convexity. The functions convex in this sense behave in many aspects similarly to ordinary convex functions. In this paper support-type properties are investigated. Using osculatory interpolation, the existence of support-like functions is established for functions convex with respect to Chebyshev systems. Unique supports are determined. A characterization of the generalized convexity via support properties is presented. 相似文献
110.
Gravity‐driven Stokes flow down an inclined plane over and around multiple obstacles is considered. The flow problem is formulated in terms of a boundary integral equation and solved using the boundary element method. A Hermitian radial basis function (RBF) is used for the interpolation of the free surface, generation of the unit normal and curvature, and to prescribe the far‐field conditions. For flow over an obstacle, hemispheres are taken. For flow around an obstacle, circular cylinders are modelled and the contact angle condition on the obstacle/free surface intersection specified using the RBF formulation. Explicit profiles are produced for flow over and around two obstacles placed in various locations relative to one another. Interaction due to two obstacles is given by comparisons made with the profiles for flow over and around individual obstacles. In general, when the obstacles are separated by a sufficiently large distance the flow profiles are identical to a single obstacle analysis. For flow over and around two obstacles in‐line with the incident flow, effects of the governing parameters are examined, with variations in plane inclination angle, Bond number, obstacle size, and in the case of obstacles intersecting the free surface, static contact angle is considered. Finally flows over and around three obstacles are modelled. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献