## Linear Operators: Spectral theory |

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Page 1600

meets the

the function q is twice differentiable , and let ( 2 , u ) be an open interval which

does not meet the

meets the

**essential spectrum**of 1 ( Hartman and Putnam [ 2 ] ) . ( 36 ) Supposethe function q is twice differentiable , and let ( 2 , u ) be an open interval which

does not meet the

**essential spectrum**of 1 but whose end points belong to the ...Page 1610

( 11 ) If i has the form [ * * ] , where all the coefficients are real and ( 1 / Pn ) ' , Pn -

1 , . . . , Po are summable in [ 0 , 0 ) , then the

interval [ 0 , 0 ) is the positive semi - axis ( Naimark [ 5 ] ) . ( 12 ) Let [ a , b ) = [ 0 , 0

) .

( 11 ) If i has the form [ * * ] , where all the coefficients are real and ( 1 / Pn ) ' , Pn -

1 , . . . , Po are summable in [ 0 , 0 ) , then the

**essential spectrum**of r in theinterval [ 0 , 0 ) is the positive semi - axis ( Naimark [ 5 ] ) . ( 12 ) Let [ a , b ) = [ 0 , 0

) .

Page 1613

The

the complex plane which coincides with the

adjoint operator in the conjugate space . The

The

**essential spectrum**is to be defined as in Section 6 , and is a closed subset ofthe complex plane which coincides with the

**essential spectrum**of the formaladjoint operator in the conjugate space . The

**essential spectrum**of a formal ...### What people are saying - Write a review

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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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 Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero