Download e-book for kindle: Introduction to Pseudodifferential and Fourier Integral by Jean-François Treves By Jean-François Treves

ISBN-10: 0306404044

ISBN-13: 9780306404047

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1 8) PROOF. We must show that Fu is C00 in the neighborhood of any point (xo, t°) E 0 X (�n \{0}) such that (4. 1 9) V( y, 17) E WF ( u ), 6 E �no if (x0, y, 6) E � cl>• then either C ,e

L'o(

1 8) can be rewritten in an interesting manner when the symbol P(x, t) of P(x, D) is positive-homogeneous (of degree m ) with respect to g, for large I t ! Indeed, we then have, for large p (and x in JC, say), p<"')( x, p acfJ (x )) = p m -l a lp<"'l( x, acfJ (x )) . (3 . 3 1 ) We know that W (c/J ; p, D) u is a polynomial with respect to p of degree "' � l a l/2. We may therefore reorder the series on the right-hand side of (3 . 1 8) as a power series in p (the powers are of the form m j, j = 0 , 1 , .