Kitabın içinden
86 sonuçtan 1-3 arası sonuçlar
Sayfa 639
We prove that the set Q = U U { v , u } llul | s1 | | 0 | | 51 is bounded . Since H is a
Hilbert space , it suffices to prove that Q is weakly bounded . Let fe H . Then f = f +
- f - , where ft , f - EK * . We prove that l ( f , x ) = | | $ + | | + | | f - 11 for all x e Q ...
We prove that the set Q = U U { v , u } llul | s1 | | 0 | | 51 is bounded . Since H is a
Hilbert space , it suffices to prove that Q is weakly bounded . Let fe H . Then f = f +
- f - , where ft , f - EK * . We prove that l ( f , x ) = | | $ + | | + | | f - 11 for all x e Q ...
Sayfa 640
1 ) n = 1 We prove that these definitions are unambiguous . Let cos ( K ) > 0 .
Then the relations - B ( u ) E - KC - K * imply that B } ( u ) = Bx ( - 8k ( u ) ) = 0 .
Therefore , the sums ( 4 . 1 ) and ( 5 . 1 ) are formed from finitely many terms .
1 ) n = 1 We prove that these definitions are unambiguous . Let cos ( K ) > 0 .
Then the relations - B ( u ) E - KC - K * imply that B } ( u ) = Bx ( - 8k ( u ) ) = 0 .
Therefore , the sums ( 4 . 1 ) and ( 5 . 1 ) are formed from finitely many terms .
Sayfa 652
We prove the inclusion k = 1 Let P , ( 9 ) » ( « ÜP - 10 ) we ( aŮ Pzlana ) I k =
Then ( W , V ) , ( 2 ) = 0 for ve Ps ( k ) + . ... Wk . Therefore Ě * Uk € _ ( 12 ) , and
hence Ě * Thus we have proved continuity of the operator & * : P : ( 12 ) + - Ú } (
92 ) .
We prove the inclusion k = 1 Let P , ( 9 ) » ( « ÜP - 10 ) we ( aŮ Pzlana ) I k =
Then ( W , V ) , ( 2 ) = 0 for ve Ps ( k ) + . ... Wk . Therefore Ě * Uk € _ ( 12 ) , and
hence Ě * Thus we have proved continuity of the operator & * : P : ( 12 ) + - Ú } (
92 ) .
Kullanıcılar ne diyor? - Eleştiri yazın
Her zamanki yerlerde hiçbir eleştiri bulamadık.
İçindekiler
HADAMARDS CONJECTURE | 634 |
Necessary facts about Sobolev spaces | 643 |
Elliptic differential inequalities | 655 |
Telif Hakkı | |
5 diğer bölüm gösterilmiyor
Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
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