## Linear Operators: Spectral theory |

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Page 1318

Suppose that the homogeneous system

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

variable s )

...

Suppose that the homogeneous system

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

variable s )

**obtained**by substituting a ; and po for & ; and Pi in [ t ] . The function K...

Page 1619

Then the spectrum of a self adjoint extension of the operator t on the interval [ 0 ,

0 )

continuous spectrum covering the positive real semi - axis , and a sequence of ...

Then the spectrum of a self adjoint extension of the operator t on the interval [ 0 ,

0 )

**obtained**by the imposition of a boundary condition at zero will consist of acontinuous spectrum covering the positive real semi - axis , and a sequence of ...

Page 1623

on the interval [ 0 , 00 ) ( cf . the end of Section 5 )

boundary condition B ( f ) = f ' ( 0 ) = 0 , namely i po da u ( [ a , b ] ) = a Java Let p

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

that ...

on the interval [ 0 , 00 ) ( cf . the end of Section 5 )

**obtained**by imposing theboundary condition B ( f ) = f ' ( 0 ) = 0 , namely i po da u ( [ a , b ] ) = a Java Let p

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

that ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero