St. Petersburg Mathematical Journal, 16. ciltAmerican Mathematical Society, 2005 |
Kitabın içinden
82 sonuçtan 1-3 arası sonuçlar
Sayfa 31
... estimate is proved for Co ( R3 ) 4 - functions , but it is known ( see , e.g. , [ 7 , p . 12 ] ) that such functions are dense in H1 ( R3 ) 4 . As a consequence , we obtain the estimate || D ( 41W ) || 0 , R3 ≤ C2 || ( D + V ) ( 41w ) ...
... estimate is proved for Co ( R3 ) 4 - functions , but it is known ( see , e.g. , [ 7 , p . 12 ] ) that such functions are dense in H1 ( R3 ) 4 . As a consequence , we obtain the estimate || D ( 41W ) || 0 , R3 ≤ C2 || ( D + V ) ( 41w ) ...
Sayfa 162
... estimate while ( 5.39 ) yields m m = 1 m = 1 Év Σ v ( Um ) 2 = Ź ( Σ » ? ) * m = 1 m = 1 \ iЄIm } 1 १ < { N } . m = 1 114 119 = v < { N } . 2m m = 1 To estimate l , we use the second inequality in ( 5.38 ) to obtain ( -1 ) N - ' < ΣΣΣ ...
... estimate while ( 5.39 ) yields m m = 1 m = 1 Év Σ v ( Um ) 2 = Ź ( Σ » ? ) * m = 1 m = 1 \ iЄIm } 1 १ < { N } . m = 1 114 119 = v < { N } . 2m m = 1 To estimate l , we use the second inequality in ( 5.38 ) to obtain ( -1 ) N - ' < ΣΣΣ ...
Sayfa 243
... estimate the norm of the operator X1 ( x2 ) . By the upper estimate ( 1.1 ) ( with j = 1 ) , we have ( 3.10 ) || X1 ( x2 ) || L2 ( 0,1 ) → L2 ( 0,1 ) ≤ sup ( 91 ( x1 , x2 ) ) 1 / 2 ≤ c1 / 2 0 < 1 < 1 for all x2 € ( 0 , a ) . As in ...
... estimate the norm of the operator X1 ( x2 ) . By the upper estimate ( 1.1 ) ( with j = 1 ) , we have ( 3.10 ) || X1 ( x2 ) || L2 ( 0,1 ) → L2 ( 0,1 ) ≤ sup ( 91 ( x1 , x2 ) ) 1 / 2 ≤ c1 / 2 0 < 1 < 1 for all x2 € ( 0 , a ) . As in ...
İçindekiler
ISOMETRIC EMBEDDINGS OF FINITEDIMENSIONAL SPACES | 17 |
CONTENTS | 27 |
1 Introduction | 117 |
Telif Hakkı | |
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analytic apply approximation assume asymptotic belongs BKN-equation block boundary bounded called closed coefficients compatible complete components condition Consequently consider constant construction contains continuous corresponding covering defined definition denote differential domain edge eigenvalues embedding equal equation estimate example exists extension fact fibers field finite fixed formula function given graph harmonic implies inequality integral 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 transl true unique values vector vertex vertices zero