## Linear Operators: Spectral theory |

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Page 1414

22 COROLLARY . Let there be given the second order differential operator d2 T =

C ) - 240 dt2 on an interval of the form [ a , b ) , where a < b < 00. Assume that ( a )

qlt ) is positive for t

22 COROLLARY . Let there be given the second order differential operator d2 T =

C ) - 240 dt2 on an interval of the form [ a , b ) , where a < b < 00. Assume that ( a )

qlt ) is positive for t

**sufficiently**near b , and ( b ) for x**sufficiently**near b , ( g ( t ) ...Page 1449

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. for ao

void . ( d ) If q ( t ) + -00 , if q is monotone decreasing for

) ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. for ao

**sufficiently**large , and if 19 ( t ) - % dt < 0 < 0 for a ,**sufficiently**large , then o ( t ) isvoid . ( d ) If q ( t ) + -00 , if q is monotone decreasing for

**sufficiently**large t , if g ( t) ...

Page 1450

( g ( t ) ' ) S1600 ) ' 9 ' ( 1 ) 7 ( t ) / 3 / 2 dt < 8 4 9 ( t ) 5/2 for

and if S. ig ( t ) 1 - Ydt < 0 for

as t = 0 , g ( t ) is monotone decreasing for

9 ...

( g ( t ) ' ) S1600 ) ' 9 ' ( 1 ) 7 ( t ) / 3 / 2 dt < 8 4 9 ( t ) 5/2 for

**sufficiently**small bo ,and if S. ig ( t ) 1 - Ydt < 0 for

**sufficiently**small bo , then oe ( t ) is void . ( d ) If g ( t )as t = 0 , g ( t ) is monotone decreasing for

**sufficiently**small t , q ' ( t ) 1 S. " ( 102 )9 ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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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 complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero