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Sayfa 670
Further , let Dn ( Rd ) be the partition of Rd obtained by extending the partition of
the basic cube lo = [ 0 , 1 ] ' into 2nd congruent parts ; then let D ( Rd ) : = UM , Dn
( Rd ) . Each subcube QE D ( Rd ) is determined by the edge length , say 2 - " ...
Further , let Dn ( Rd ) be the partition of Rd obtained by extending the partition of
the basic cube lo = [ 0 , 1 ] ' into 2nd congruent parts ; then let D ( Rd ) : = UM , Dn
( Rd ) . Each subcube QE D ( Rd ) is determined by the edge length , say 2 - " ...
Sayfa 673
Here Un ( Q ) is a partition of the subcube Q into nd equal cubes ( thus , Dr = U2r
( lo ) ) . This result was obtained in [ 22 ] for d = 1 ( see [ 23 ] for details ) ; the
method of proof used there generalizes to the multidimensional situation [ 24 ] .
Here Un ( Q ) is a partition of the subcube Q into nd equal cubes ( thus , Dr = U2r
( lo ) ) . This result was obtained in [ 22 ] for d = 1 ( see [ 23 ] for details ) ; the
method of proof used there generalizes to the multidimensional situation [ 24 ] .
Sayfa 756
According to ( 2 . 5 ) , 15 ; ( 0 ) | Y1 , j ( t ) is nonzero for given j only when 1 € N : =
{ t : nu ( t ) E 1 ; for some v = 1 , . . . , 1 } . The sets { N n O ( t ) } ten form a partition
N = N ( 1 ) U . . . UN ( k ) ( where N ( p ) n N ( q ) = Ø for p + 9 ) , and the sets ( p ) ...
According to ( 2 . 5 ) , 15 ; ( 0 ) | Y1 , j ( t ) is nonzero for given j only when 1 € N : =
{ t : nu ( t ) E 1 ; for some v = 1 , . . . , 1 } . The sets { N n O ( t ) } ten form a partition
N = N ( 1 ) U . . . UN ( k ) ( where N ( p ) n N ( q ) = Ø for p + 9 ) , and the sets ( p ) ...
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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