## Linear Operators: Spectral theory |

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Page 1318

Suppose that the homogeneous system

has a non - trivial solution q ? ( c ) , B7 ( c ) , and let K. ( . ) be the function ( of the

variable 8 )

...

Suppose that the homogeneous system

**obtained**from equations [ 1 ' ] and [ 2 ' )has a non - trivial solution q ? ( c ) , B7 ( c ) , and let K. ( . ) be the function ( of the

variable 8 )

**obtained**by substituting ap and go for Qi and Bi in [ t ] . The function K...

Page 1623

To ( ) " ( dt ) on the interval [ 0 , 0 ) ( cf. the end of Section 5 )

imposing the boundary condition B ( f ) = f ' ( 0 ) = 0 , namely 1 da u ( [ a , b ] ) N va

Let p be a positive Borel measure on the positive real axis , and let o = p - u .

Suppose ...

To ( ) " ( dt ) on the interval [ 0 , 0 ) ( cf. the end of Section 5 )

**obtained**byimposing the boundary condition B ( f ) = f ' ( 0 ) = 0 , namely 1 da u ( [ a , b ] ) N va

Let p be a positive Borel measure on the positive real axis , and let o = p - u .

Suppose ...

Page 1624

In the same way , the functions cos tvā

property Locos svā cos tvāu ( da ) = 0 , $ + t . ... Their first step consists in

cos tvī in ...

In the same way , the functions cos tvā

**obtained**from the operator to enjoy theproperty Locos svā cos tvāu ( da ) = 0 , $ + t . ... Their first step consists in

**obtaining**an expression for f ( t , 2 ) as a “ linear combination ” of the functionscos tvī in ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### 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