## Linear Operators: Spectral theory |

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Page 1541

Nelson Dunford, Jacob T. Schwartz. Show that the

the half - plane { 2 \ R2 > 0 } . B5 Given the Sturm - Liouville operator T = - ( d / dt )

p ( t ) ( d / dt ) + a ( t ) on the interval [ 0 , 0 ) ( p positive , q real ) , suppose that ...

Nelson Dunford, Jacob T. Schwartz. Show that the

**essential spectrum**of t lies inthe half - plane { 2 \ R2 > 0 } . B5 Given the Sturm - Liouville operator T = - ( d / dt )

p ( t ) ( d / dt ) + a ( t ) on the interval [ 0 , 0 ) ( p positive , q real ) , suppose that ...

Page 1595

Other criteria for the determination of the

) Under the assumptions ( a ) and ( b ) of ( 5 ) , and with the further assumption

that for all x t ) g ( t ) / - 1 / 2 dt = 00 , the

Other criteria for the determination of the

**essential spectrum**are the following : ( 9) Under the assumptions ( a ) and ( b ) of ( 5 ) , and with the further assumption

that for all x t ) g ( t ) / - 1 / 2 dt = 00 , the

**essential spectrum**of 7 is the entire real ...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 |

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