نتایج جستجو برای: spherical mean operator

تعداد نتایج: 720046  

Journal: :Proceedings of the American Mathematical Society 2018

Journal: :Journal of Mathematical Inequalities 2015

Journal: :Journal of Mathematical Inequalities 2016

Journal: :Journal of Inequalities and Applications 2018

2016
Zhendong Luo

In this study, a high accuracy numerical method based on the spectral theory of compact operator for biharmonic eigenvalue equations on a spherical domain is developed. By employing the orthogonal spherical polynomials approximation and the spectral theory of compact operator, the error estimates of approximate eigenvalues and eigenfunctions are provided. By adopting orthogonal spherical base f...

Journal: :SIAM J. Numerical Analysis 2012
Congpei An Xiaojun Chen Ian H. Sloan Robert S. Womersley

Abstract. We consider polynomial approximation on the unit sphere S = {(x, y, z) ∈ R : x + y + z = 1} by a class of regularized discrete least squares methods, with novel choices for the regularization operator and the point sets of the discretization. We allow different kinds of rotationally invariant regularization operators, including the zero operator (in which case the approximation includ...

2002
Alexander G. Ramm

Let S be a surface in R which divides the space into two connected components D1 and D2. Let f ∈ C0(R) be some real-valued compactly supported function with supp f ⊂ D1. Consider Mf := m(y, r) := ∫ Rn f(z)δ(|y − z| − r)dz, where δ is the delta-function, y ∈ S and r > 0 are arbitrary. A general, local at infinity, condition on S is given, under which M is injective, that is, Mf = 0 implies f = 0...

2011
Shaobo Lin Feilong Cao

In the paper titled as “Jackson-type inequality on the sphere” 2004 , Ditzian introduced a spherical nonconvolution operator Ot,r , which played an important role in the proof of the wellknown Jackson inequality for spherical harmonics. In this paper, we give the lower bound of approximation by this operator. Namely, we prove that there are constants C1 and C2 such that C1ω2r f, t p ≤ ‖Ot,rf − ...

Journal: :Int. J. Comput. Geometry Appl. 2006
Guoliang Xu

In this paper we first modify a widely used discrete Laplace Beltrami operator proposed by Meyer et al over triangular surfaces, and then establish some convergence results for the modified discrete Laplace Beltrami operator over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace Beltra...

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