Kitabın içinden
81 sonuçtan 1-3 arası sonuçlar
Sayfa 307
The operator in L2 ( II ) that we consider is formally given by the expression ( 0 . 3
) ( 6 ( x ) ) + ( ( D - A ( x ) ) * g ( x ) ( D – A ( x ) ) + V ( x ) ) ( 6 ( x ) ) - 1 with
coefficients periodic along the waveguide . The conditions on the coefficients are
similar ...
The operator in L2 ( II ) that we consider is formally given by the expression ( 0 . 3
) ( 6 ( x ) ) + ( ( D - A ( x ) ) * g ( x ) ( D – A ( x ) ) + V ( x ) ) ( 6 ( x ) ) - 1 with
coefficients periodic along the waveguide . The conditions on the coefficients are
similar ...
Sayfa 336
By Proposition 3 . 5 , the form în is lower semibounded and closable in L2 ( S ) .
Then ( 4 . 46 ) and ( 4 . 47 ) imply that the form m . is lower semibounded and
closable in L2 ( II . ) . The closed form m + gives rise to a selfadjoint operator M .
in L2 ...
By Proposition 3 . 5 , the form în is lower semibounded and closable in L2 ( S ) .
Then ( 4 . 46 ) and ( 4 . 47 ) imply that the form m . is lower semibounded and
closable in L2 ( II . ) . The closed form m + gives rise to a selfadjoint operator M .
in L2 ...
Sayfa 341
In the direct integral expansion for the periodic operator in L2 ( R2 ) , an operator
family M ( k ) arises that depends on the two - dimensional parameter k = ( ki , k2 )
E R2 . Under our assumptions on the coefficients , such an operator family was ...
In the direct integral expansion for the periodic operator in L2 ( R2 ) , an operator
family M ( k ) arises that depends on the two - dimensional parameter k = ( ki , k2 )
E R2 . Under our assumptions on the coefficients , such an operator family was ...
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algebraic analytic apply assume basis boundary bounded called chain homotopy closed coefficients complex computation condition connection Consequently consider constant construction contains continuous convex corresponding defined definition deformation denote determined differential domain element equal equation equivalence estimate example exists extension fact field finite fixed formula function given identity implies inequality integral intersection introduce invariant inverse isomorphism Lemma linear Math Mathematical matrix measure metric Moreover natural normal Observe obtain Obviously operator orientation particular periodic positive present problem projective Proof properties Proposition prove regular relation Remark respectively result ring satisfies scheme sequence singular smooth solutions space standard statement Subsection suffices Suppose takes Theorem theory transformation true twists unique vector weight zero