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86 sonuçtan 1-3 arası sonuçlar
Sayfa 40
We define the operator M ( z ) outside this spectrum by the formula ( 3 . 9 ) M ( ) =
| V | 1 / 2 ( Lo – z ) - 4V / 1 / 2 ( cf . ( 2 . 17 ) ) . A priori , it is defined on H1 / 2 ( 12 )
4 , but it extends to a bounded operator on H° ( 12 ) 4 by the formula ( 3 .
We define the operator M ( z ) outside this spectrum by the formula ( 3 . 9 ) M ( ) =
| V | 1 / 2 ( Lo – z ) - 4V / 1 / 2 ( cf . ( 2 . 17 ) ) . A priori , it is defined on H1 / 2 ( 12 )
4 , but it extends to a bounded operator on H° ( 12 ) 4 by the formula ( 3 .
Sayfa 42
Clearly , this is an operator bounded uniformly in s . Finally , 7 ( Lo – z ) - 1 = { yLo
? } { Lo ( Lo + is ) - 1 } , and we see that this is a uniformly bounded operator from
H° ( 12 ) 4 to Ho ( T ) 4 , so that the adjoint operator from H° ( ) 4 to H° ( 12 ) 4 is ...
Clearly , this is an operator bounded uniformly in s . Finally , 7 ( Lo – z ) - 1 = { yLo
? } { Lo ( Lo + is ) - 1 } , and we see that this is a uniformly bounded operator from
H° ( 12 ) 4 to Ho ( T ) 4 , so that the adjoint operator from H° ( ) 4 to H° ( 12 ) 4 is ...
Sayfa 225
Therefore , the operators 19 = 7 - 1 and 7 = 7 % - 1 are bounded on L ? with the
bound | | 7 ? | | L2 < C | | A | | - - 1 - H1 by Lemma 5 . 2 , and ( 5 . 20 ) and similarly
for 79 . Moreover , the quantities | | A1 | | - 14H1 , € > 0 , are bounded uniformly ...
Therefore , the operators 19 = 7 - 1 and 7 = 7 % - 1 are bounded on L ? with the
bound | | 7 ? | | L2 < C | | A | | - - 1 - H1 by Lemma 5 . 2 , and ( 5 . 20 ) and similarly
for 79 . Moreover , the quantities | | A1 | | - 14H1 , € > 0 , are bounded uniformly ...
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İçindekiler
ISOMETRIC EMBEDDINGS OF FINITEDIMENSIONAL loSPACES | 23 |
Dedicated to M Sh Birman on the occasion of his 75th birthday | 285 |
ABSTRACT The nonexistence of isometric embeddings em line with p q is proved | 296 |
Telif Hakkı | |
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analytic apply approximation assume asymptotic belongs BKN-equation block boundary bounded called closed coefficients collection compatible complete components condition Consequently consider constant construction contains continuous corresponding covering defined definition denote differential domain edge eigenvalues embedding English equal equation estimate example exists extension fact fibers field finite fixed formula function given graph harmonic identity implies inequality integral introduce invertible Lemma linear manifold Math Mathematical matrix monodromy Moreover norm obtain operator oriented pair particular periodic polynomial positive potential present problem proof properties Proposition prove rational relation Remark representation respect result satisfies selfadjoint separation singular smooth solution space spectral spectrum statement Subsection sufficiently Suppose surface symmetric Theorem theory transformation transl true unique values vector vertex vertices zero