## Linear Operators: Spectral theory |

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Page 1099

By elementary arguments such as those employed in the third paragraph of the

proof of Lemma 6 , which we leave to the reader to elaborate in detail , we may

conclude that to establish ( a ) in general it is

By elementary arguments such as those employed in the third paragraph of the

proof of Lemma 6 , which we leave to the reader to elaborate in detail , we may

conclude that to establish ( a ) in general it is

**sufficient**to consider the case in ...Page 1440

240 ) ( ) + c . ( dt ) j = 1 We will first show that for c

real and positive . Passing by means of Theorem 4 to a

small subinterval [ ao , b ) of ( 1440 ORDINARY DIFFERENTIAL OPERATORS

XIII .

240 ) ( ) + c . ( dt ) j = 1 We will first show that for c

**sufficiently**large ... Let 2o bereal and positive . Passing by means of Theorem 4 to a

**sufficient**( 2n ) 1 77 lysmall subinterval [ ao , b ) of ( 1440 ORDINARY DIFFERENTIAL OPERATORS

XIII .

Page 1450

60 / q ' ( t ) \ Jo I 19 ( t ) / 3 / 2 ) ( 1 ) ° / for

dt < 4 * lạ ( t ) 5 / 2 | lig ( t ) | - % dt < 0 for

( d ) If q ( t ) + - 00 as t → 0 , qlt ) is monotone decreasing for

60 / q ' ( t ) \ Jo I 19 ( t ) / 3 / 2 ) ( 1 ) ° / for

**sufficiently**small bo , and if 1 ( 9 ( t ) ' ) ? ,dt < 4 * lạ ( t ) 5 / 2 | lig ( t ) | - % dt < 0 for

**sufficiently**small bo , then oe ( t ) is void .( d ) If q ( t ) + - 00 as t → 0 , qlt ) is monotone decreasing for

**sufficiently**small t ...### What people are saying - Write a review

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider 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 multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero