## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1154

Since the product group R ( 2 ) = RX R is locally compact and o - compact , it has

a Haar measure 2 ( 2 ) defined on its Borel field ( 2 ) and what we shall prove is

that for some

Since the product group R ( 2 ) = RX R is locally compact and o - compact , it has

a Haar measure 2 ( 2 ) defined on its Borel field ( 2 ) and what we shall prove is

that for some

**constant**c , ( R ( 2 ) , E ( 2 ) , 2 ( 2 ) ) = c ( R , E , a ) ( R , E , 2 ) .Page 1176

Subtracting a suitable

suppose without loss of generality that kn ... here we have used the uniform

boundedness of the functions kn and of their variations to conclude that the

Subtracting a suitable

**constant**cn from each of the functions kn , we maysuppose without loss of generality that kn ... here we have used the uniform

boundedness of the functions kn and of their variations to conclude that the

**constants**en are ...Page 1599

( 32 ) On the interval [ 0 , 00 ) , if g ( t ) tends monotonically to -00 , and if -9 ( t ) <

Ct for large t , then there exists a

every interval of length K contains a point of the essential spectrum of 1 (

Hartman ...

( 32 ) On the interval [ 0 , 00 ) , if g ( t ) tends monotonically to -00 , and if -9 ( t ) <

Ct for large t , then there exists a

**constant**K ( depending only on C ) such thatevery interval of length K contains a point of the essential spectrum of 1 (

Hartman ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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### Common terms and phrases

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 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