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u(t, x), x M , be the lowest eigenfunction of the Schrödinger op-erator R 1.

Also inisotropic models one can have difference-differential equations if there is a matter degreeof freedom such as a scalar, but the crucial difference here is that there are differential

ÕP j }i:f [ i V3{bWqj8Wj)jr[ Yyi_6_ Ws i V | T X _ W z[¢j i jVJ{ i [ X _ WYVJWs[ X XF :@ , F. ... 1 i n z# 1 =4 _ 4 6 7 Õ> i n z#T$ % D 62 Õ!PD i n z#T$ % D =62 ÕP.

explanation for the nonmonotonuous ts dependence of the decay curves. It is clear thatwith inreasing ts we reach larger θm for the same ǫp, which is reflected in more oscillations.

Thus, the op-erator appearing there is an isomorphism for all nearby V ’s.

2.2) under theopposite of the partial order of inclusion, op; whence, the same is true of Bx; Because B is a basis for the topology of X, Bx is cofinal ... system of L-structures over 〈Bx, op 〉. Definition 3.6 With notation as above, for x X, the

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"#$ %'&(),). -/.01)24357698;:=<>?@.BACEDF6HGI8J:KML=DN6H3(OP.Q$.-/.BR%SSN6T:UVXWY Z[V]__ba%_dceY+]Ff7gihjgi[/W khmlInoghqprfs_tceuwvIhmkxyNorz{]F[}|7fdXna;v/_vI[uwvIhmkxyFojz{]u+'. gbnp_7k

Typically, an operator in Op hS(q,p,p′) with p < 0 and p′ < 0 is compact. ... 12 (2.35). is an h-pseudodifferential operator. More precisely it belongs to Op hS(0,0,0).

compact for all g C0(X). 4.3. Denote the algebra of all locally compact, finite propagation op-.