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1THE HOMOGENEOUS POLYNOMIAL SOLUTIONS FOR THE GRUSHIN OPERATOR显示文摘In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.刘海蓉 2018Acta Mathematica Scientia2018,38,1:0
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