## Linear Operators: Spectral theory |

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Results 1-3 of 73

Page 1449

for do

0e ( T ) is void . ( d ) If a ( t ) → - 00 , if q is monotone decreasing for

large t , if 1 g ( t ) ' \ 1 ( g ( t ) ) " dt < 0 Tg ( t ) 13 / 2 ) = g ( + ) 5 / 2 for ao

...

for do

**sufficiently**large , and if Ig ( t ) - % dt < 00 Jao for a ,**sufficiently**large , then0e ( 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

and if lig ( t ) - " edt < 0 for

00 as t + 0 , g ( t ) is monotone decreasing for

...

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

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 rangedense 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