By S. Zaidman

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**Example text**

D) L is an elliptic operator, with Coo-coefficients. That is, we have O. 3) implies cplx=0 assuming T real-valued. Real characteristics do not exist. oxn . , e) L = P(D) is a constant coefficient hyperbolic operator (cf. ), with respect to some given real vector h# 0. 9. 5. ,n . The characteristic equation is of the form PN((plx)=0. ,0,1), as always may be achieved by a linear transformation of independent variables. 15) will give its own family of characteristic surfaces and bicharacteristics.

7). 9) is replaced by elx . 1 follows. 4. 13) Ka (supp v x supp w)fl{jx+yIsa} is compact for every a>0 . Here supp v and supp w are regarded as subsets of in of the variables x and y, respectively (cf. [Schwl] or [C1], 1,8). 13) holds under these assumptions. Moreover, P(D)v=g follows, leading to a solution of the free space problem, and the related initial-boundary problems. , , Now let us attempt a detailed construction of the proper e. , the potential equation Au=f. For n2:3 the function -IX is Lpol, hence a distribution in S'.