Linear Operators: Spectral theory |
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Page 993
Then it follows from what has just been demonstrated that ay , = Qyuv , = Qy , i . e
. , Qy is independent of V . Q . E . D . 16 THEOREM . If the bounded measurable
function o has its spectral set consisting of the single point m then , for some ...
Then it follows from what has just been demonstrated that ay , = Qyuv , = Qy , i . e
. , Qy is independent of V . Q . E . D . 16 THEOREM . If the bounded measurable
function o has its spectral set consisting of the single point m then , for some ...
Page 996
1 ( d ) it follows from the above equation that f * 4 0 . From Lemma 12 ( b ) it is
seen that olf * ) Colp ) and from Lemma 12 ( c ) and the equation of = tf it follows
that olf * 9 ) contains no interior point of o ( 9 ) . Hence of * ) is a closed subset of
the ...
1 ( d ) it follows from the above equation that f * 4 0 . From Lemma 12 ( b ) it is
seen that olf * ) Colp ) and from Lemma 12 ( c ) and the equation of = tf it follows
that olf * 9 ) contains no interior point of o ( 9 ) . Hence of * ) is a closed subset of
the ...
Page 1486
If follows immediately that all the coefficients of t are bounded ; thus , by Theorem
6 . 35 , it follows that t has no boundary values at + 00 or at – 00 . By Theorem 2 .
19 , T has no boundary values . Thus , by Definition 2 . 17 every linear ...
If follows immediately that all the coefficients of t are bounded ; thus , by Theorem
6 . 35 , it follows that t has no boundary values at + 00 or at – 00 . By Theorem 2 .
19 , T has no boundary values . Thus , by Definition 2 . 17 every linear ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
15 other sections not shown
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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero