## Linear Operators: Spectral theory |

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Page 1191

However , this

that any function g with a continuous first derivative has the property that lit , 8 ) =

( 1 , 2 3 ) , fed ( ia ) , dt and thus any such g , even though it fails to vanish at one ...

However , this

**operator**is not self**adjoint**for it is clear from the above equationsthat any function g with a continuous first derivative has the property that lit , 8 ) =

( 1 , 2 3 ) , fed ( ia ) , dt and thus any such g , even though it fails to vanish at one ...

Page 1270

The problem of determining whether a given symmetric

theorem may be employed . If the answer to this problem is affirmative , it is

important to ...

The problem of determining whether a given symmetric

**operator**has a self**adjoint**extension is of crucial importance in determining whether the spectraltheorem may be employed . If the answer to this problem is affirmative , it is

important to ...

Page 1548

very . extensions of S and Ŝ respectively , and let 2 , ( T ) and an ( f ) be the

numbers defined for the self adjoint operators T and T as in Exercise D2 . Show

that an ( T ) 2 An ( Î ) , n 2 1 . Dii Let T , be a self

H , ...

very . extensions of S and Ŝ respectively , and let 2 , ( T ) and an ( f ) be the

numbers defined for the self adjoint operators T and T as in Exercise D2 . Show

that an ( T ) 2 An ( Î ) , n 2 1 . Dii Let T , be a self

**adjoint operator**in Hilbert spaceH , ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 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 operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero