Linear Operators: Spectral theory |
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Page 1449
for do sufficiently large , and if Ig ( t ) - % dt < 00 Jao for a , sufficiently large , then
0e ( T ) is void . ( d ) If a ( t ) → - 00 , if q is monotone decreasing for sufficiently
large t , if 1 g ( t ) ' \ 1 ( g ( t ) ) " dt < 0 Tg ( t ) 13 / 2 ) = g ( + ) 5 / 2 for ao sufficiently
...
for do sufficiently large , and if Ig ( t ) - % dt < 00 Jao for a , sufficiently large , then
0e ( T ) is void . ( d ) If a ( t ) → - 00 , if q is monotone decreasing for sufficiently
large t , if 1 g ( t ) ' \ 1 ( g ( t ) ) " dt < 0 Tg ( t ) 13 / 2 ) = g ( + ) 5 / 2 for ao sufficiently
...
Page 1450
pbo q ' ( t ) q ( t ) ' ) 21 1 dt < ( t ) 5 / 2 0 Jo I 19 ( t ) / 3 / 2 for sufficiently small bo ,
and if lig ( t ) - " edt < 0 for sufficiently small bo , then oe ( T ) is void . ( d ) If a ( t ) -
00 as t + 0 , g ( t ) is monotone decreasing for sufficiently small t , bol g ' ( t ) \ 1 - 1
...
pbo q ' ( t ) q ( t ) ' ) 21 1 dt < ( t ) 5 / 2 0 Jo I 19 ( t ) / 3 / 2 for sufficiently small bo ,
and if lig ( t ) - " edt < 0 for sufficiently small bo , then oe ( T ) is void . ( d ) If a ( t ) -
00 as t + 0 , g ( t ) is monotone decreasing for sufficiently small t , bol g ' ( t ) \ 1 - 1
...
Page 1760
... bounded and of norm at most Me We shall show that ( vii ) for each k 20 , and
for each sufficiently small positive a sa ( k ) , the mapping 1 - aSk has a range
dense in Ħ * ) ( C ) . Suppose that ( v ) is false , but that ( vii ) has been
established .
... bounded and of norm at most Me We shall show that ( vii ) for each k 20 , and
for each sufficiently small positive a sa ( k ) , the mapping 1 - aSk has a range
dense in Ħ * ) ( C ) . Suppose that ( v ) is false , but that ( vii ) has been
established .
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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