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77 sonuçtan 1-3 arası sonuçlar
Sayfa 34
Statement 1 follows from ( 2 . 3 ) . We check statement 2 . Let wie Hy , so that the
form ( Dwi + Vw1 , W2 ) o is continuous in w2 with respect to the L2 - norm . Then
, assuming for simplicity that y is real , we have ( 2 . 5 ) ( D ( ywi ) + VyW1 , W2 ) ...
Statement 1 follows from ( 2 . 3 ) . We check statement 2 . Let wie Hy , so that the
form ( Dwi + Vw1 , W2 ) o is continuous in w2 with respect to the L2 - norm . Then
, assuming for simplicity that y is real , we have ( 2 . 5 ) ( D ( ywi ) + VyW1 , W2 ) ...
Sayfa 131
Hence , taking into account the asymptotic properties of the Sibuya function M ( 1
, 2 ) ( see statement 2 of Theorem 4 ) , we arrive at the asymptotic relation ( iii ) .
To obtain ( ii ) , we note that for every fixed x we have det Vo ( 1 , 2 ) — 1 , 1 0 ...
Hence , taking into account the asymptotic properties of the Sibuya function M ( 1
, 2 ) ( see statement 2 of Theorem 4 ) , we arrive at the asymptotic relation ( iii ) .
To obtain ( ii ) , we note that for every fixed x we have det Vo ( 1 , 2 ) — 1 , 1 0 ...
Sayfa 222
Note that statement ( 5 . 3 ) is equivalent to the statement in Theorem 3 . 3 . The (
+ ) part of statement ( 5 . 3 ) is trivial : if E ! ( Vzyelz = ze ) = 0 , then 0 , 0c ( z ) ] z =
ze = ( OzVzye , E ( Vzye ) } \ z = ze = ( OzVzyelz = z < , E ( Uzye ) ] z = ze ) = 0 .
Note that statement ( 5 . 3 ) is equivalent to the statement in Theorem 3 . 3 . The (
+ ) part of statement ( 5 . 3 ) is trivial : if E ! ( Vzyelz = ze ) = 0 , then 0 , 0c ( z ) ] z =
ze = ( OzVzye , E ( Vzye ) } \ z = ze = ( OzVzyelz = z < , E ( Uzye ) ] z = ze ) = 0 .
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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