Linear Operators: Spectral theory |
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Results 1-3 of 63
Page 1099
... in T and since every finite matrix may be approximated arbitrarily closely by
non - singular matrices , it is sufficient to consider the case in which T is non -
singular . Then A = ( TT * ) 1 / 2 is also non - singular and if U = A - 17 , UU * = A ...
... in T and since every finite matrix may be approximated arbitrarily closely by
non - singular matrices , it is sufficient to consider the case in which T is non -
singular . Then A = ( TT * ) 1 / 2 is also non - singular and if U = A - 17 , UU * = A ...
Page 1584
The contemporary research of Hellinger [ 1 ] , E . Schmidt [ 1 , 2 ] and Hilbert [ 1 ]
on integral equations naturally led to an interest in a similar approach to
differential operators whose coefficients are singular at one or both of the
endpoints of ...
The contemporary research of Hellinger [ 1 ] , E . Schmidt [ 1 , 2 ] and Hilbert [ 1 ]
on integral equations naturally led to an interest in a similar approach to
differential operators whose coefficients are singular at one or both of the
endpoints of ...
Page 1919
7 ( 136 ) singular , III . 4 . 12 ( 131 ) spaces of , as conjugate spaces , IV . 5 . 1 (
258 ) , IV . 5 . 3 ( 259 ) , IV . 6 . 2 – 3 ( 262 – 264 ) , IV . 8 . 16 ( 296 ) definitions , (
160 – 162 ) , IV . 2 . 15 - 17 ( 240 ) , IV . 6 . 1 ( 261 ) remarks on , ( 389 - 390 )
study ...
7 ( 136 ) singular , III . 4 . 12 ( 131 ) spaces of , as conjugate spaces , IV . 5 . 1 (
258 ) , IV . 5 . 3 ( 259 ) , IV . 6 . 2 – 3 ( 262 – 264 ) , IV . 8 . 16 ( 296 ) definitions , (
160 – 162 ) , IV . 2 . 15 - 17 ( 240 ) , IV . 6 . 1 ( 261 ) remarks on , ( 389 - 390 )
study ...
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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