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31 sonuçtan 1-3 arası sonuçlar
Sayfa 307
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 to those imposed in ( Sh3 ] in the case of a periodic operator in L2 ( R2 ) .
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 to those imposed in ( Sh3 ] in the case of a periodic operator in L2 ( R2 ) .
Sayfa 319
12 ) , and let A ( 1 ) ( z ) be a vector - valued 71 - periodic function satisfying ( 2 .
14 ) . Suppose that a real 71 - periodic signed Borel measure du ( 1 ) on S is of
locally finite variation and satisfies conditions ( i ' ) - ( iii ' ) . Let mm ( where I and u
...
12 ) , and let A ( 1 ) ( z ) be a vector - valued 71 - periodic function satisfying ( 2 .
14 ) . Suppose that a real 71 - periodic signed Borel measure du ( 1 ) on S is of
locally finite variation and satisfies conditions ( i ' ) - ( iii ' ) . Let mm ( where I and u
...
Sayfa 328
1 is a consequence of the following theorem . Theorem 3 . 8 . Let S be the strip
defined by ( 3 . 1 ) . Let ĝ ( z ) be a measurable 71 - periodic ( 2 x 2 ) - matrix -
valued function with real - valued entries and satisfying conditions ( 3 . 40 )( 3 . 45
) .
1 is a consequence of the following theorem . Theorem 3 . 8 . Let S be the strip
defined by ( 3 . 1 ) . Let ĝ ( z ) be a measurable 71 - periodic ( 2 x 2 ) - matrix -
valued function with real - valued entries and satisfying conditions ( 3 . 40 )( 3 . 45
) .
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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