## Linear Operators: Spectral theory |

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Page 1318

Suppose that the homogeneous system

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

variable 8 )

is ...

Suppose that the homogeneous system

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

variable 8 )

**obtained**by substituting a ? and for di and Bi in [ 1 ] . The function K ,is ...

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

BAlgebras | 859 |

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 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 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