# New PDF release: An analysis of time-shared computer systems

By Allan L. Scherr

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We shall apply here the theory from [15] for the weight function cp( 0',1]) = 10'1 15 + 11]'1 15 + 11]"1. Sometimes we just write cp = cp( 1]), since we are working in the region 10'1 15 < 11]"1 where 10'1 15 + 11]'1 15 + 11]"1 rv 11]'1 15 + 11]"1. Starting point in our considerations is that the phase function w is in This phase function is not homogeneous and it is not possible in general to work with homogeneous versions of wave front sets. However, if we localize in the phase variables to sets of form {1]; 11] - ijl < clijIS}, then w has the right behavior.

Assuming for simplicity that Pu = f E CW with u E Coo, we apply the 'coercive' estimate above to v =

N' . The soIut'Ions Xj homogeneous of degrees 0 and 1 respectively. 7) r-'(0 , Y' ,y" ,'f/,, 'f/If) = (7. 6 of [15] we have that the preceding statement of propagation remains valid if we replace X by X. The proof in [15] is based on the remark that, because of the quasihomogeneity of b, the first n + 1 components of X - X have strictly negative degree, whereas the second n + 1 components have degree < 1. It follows then easily that W P;: v n X(A) = 0 if and only if W P;: v n X(A) = 0; d. 9. 11), and X(D) contains a set of form V n W~,s.