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Sayfa 899
It is easily seen that the required estimate is equivalent to w2 ( 2 - 1 ) 22 ' < + 00 .
( ii ) To estimate wp ( 2 - ) , let us again introduce cut - off functions 0x ( 5 ) = { $ ( 5
) , 2 - K 5P ( 5 ) < 2 - k + 1 , at other points , and the corresponding quantit 0p ...
It is easily seen that the required estimate is equivalent to w2 ( 2 - 1 ) 22 ' < + 00 .
( ii ) To estimate wp ( 2 - ) , let us again introduce cut - off functions 0x ( 5 ) = { $ ( 5
) , 2 - K 5P ( 5 ) < 2 - k + 1 , at other points , and the corresponding quantit 0p ...
Sayfa 1067
It is worth noting that the estimating constant in ( 3 . ... This yields estimates for the
total scattering cross - section ( 2 . 22 ) . ... ( x ) > 0 ) c ( d ) is replaced by głc ( d ) ,
and for the total cross - section an estimate in terms of Cg ? is obtained .
It is worth noting that the estimating constant in ( 3 . ... This yields estimates for the
total scattering cross - section ( 2 . 22 ) . ... ( x ) > 0 ) c ( d ) is replaced by głc ( d ) ,
and for the total cross - section an estimate in terms of Cg ? is obtained .
Sayfa 1140
For large t it is necessary to add to this estimate an estimate that is applicable for
all t ( including small t ) : llpe - iHi Pef | | 2 < | | e - ill Pcf | | ( 2 . 3 . 4 ) = | | Ee – hozi
03E * f | | 2 < c | | E * f | | 2 < cl | f | | 2 . Here the estimates of Proposition 2 . 2 .
For large t it is necessary to add to this estimate an estimate that is applicable for
all t ( including small t ) : llpe - iHi Pef | | 2 < | | e - ill Pcf | | ( 2 . 3 . 4 ) = | | Ee – hozi
03E * f | | 2 < c | | E * f | | 2 < cl | f | | 2 . Here the estimates of Proposition 2 . 2 .
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İçindekiler
HADAMARDS CONJECTURE | 634 |
Necessary facts about Sobolev spaces | 643 |
Elliptic differential inequalities | 655 |
Telif Hakkı | |
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According algebra analytic apply assertion assume asymptotic Banach space boundary bounded called closed complete condition cone connected Consequently consider const constant construction contains continuous corresponding cubes defined definition denote depend derivatives described determined differential direct domain eigenvalues element English transl equality equation equivalent estimate example exists extension fact field finite fixed follows formula function Further given gives hence holds implies inequality integral introduce lattice Lemma limit linear mapping Math Mathematical matrix means measure multiplicity norm obtained Obviously operator pair particular perturbation polynomial positive possible present principle problem Proof properties Proposition proved reduced relation remains Remark representation respect satisfies scattering side smooth solution space spectral spectrum subspace sufficiently Suppose Theorem theory unique valid vector zero