EGOROV'S THEOREM FOR A DIFFRACTIVE BOUNDARY PROBLEM
[摘要] Let (TRIANGLE) be the Laplacian on R(;;n)(FDIAG)K with Dirichlet boundary conditions. Assume K is smoothly bounded with strictly convex boundary. By the spectral theorem define e(;;itSQRT.(-)(TRIANGLE)(;; )and extend this operator to ;;(R(;;n)(FDIAG)K). Theorem. Let P (epsilon) OPS(;;m)(R(;;n)(FDIAG)K). Suppose the distribution kernel for P is compactly supported in R(;;n)(FDIAG)K X R(;;n)(FDIAG)K(xi), and (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) Then modulo a smoothing operator (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) for any 1/2 0.
[发布日期] [发布机构] Rice University
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