Microlocal energy methods and pseudo-differential operators |
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Authors: | Kiyômi Kataoka |
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Affiliation: | (1) Department of Mathematics, Faculty of Science, Tokyo Metropolitan University, Fukasawa, Setagaya-Ku, 158 Tokyo, Japan |
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Abstract: | A functionk(x, u) of the(n+n)-variables is said to be a positive Hermite kernel if, and the matrix(k(xi, xj))i,j is positive semi-definite for every integerN and everyx1, ..., xN. In this paper, we prove that this positive structure can be microlocalized in the category of microfunctions. Further we obtain a useful theorem concerning the positivity of pseudo-differential operators. This theory will play important roles in the study of analytic singularities of solutions of boundary value problems. |
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