We prove that the global symbol is truly a symbol, of the same order of its operator, and define a quantization map with which one can recover the operator (modulo smoothing operators.) We compute the global symbol for a Laplacian, and give a formula for the trace in terms of the ...
where ΔΣ is the Laplacian on the unit sphere. Equation (10.88) has to be solved under the normalization condition: (10.89)∯Σweq(m)dS=1. The solution of this problem can be obtained in closed form in the special case when: (10.90)Φ(m)=F(gL(m)), where F(g) is some sca...
second-order eigenvalue problems discretized through the (isogeometric) Galerkin method based on B-splines of degreepand smoothnessC^k,0\le k\le p-1. For each discretized problem, we compute the so-called symbol, which is a function
\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi$$\\end{document}-Laplacian...
Using it for interpolation comes down to thin plate spline interpolation [36], rotationally invariant multidimensional generalizations of the cubic spline interpolation. The higher-order nonlinear diffusion considered in this paper is related to the differential operator based on Laplacian 𝐿𝑢:=−Δ...