## Linear Operators: Spectral theory |

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Page 1120

Throughout the present section , we

Hilbert space is separable . Subdiagonal representations of an operator are

connected with the study of its invariant subspaces . Thus , the key to the situation

that we ...

Throughout the present section , we

**assume**for simplicity of statement thatHilbert space is separable . Subdiagonal representations of an operator are

connected with the study of its invariant subspaces . Thus , the key to the situation

that we ...

Page 1629

Oti ' . j = 0 éj , ig , - - - , é ; = 1 the coefficients ai . . . . it , . . . , in ) being

be defined for t = [ ty , . ... having arbitrarily prescribed values and first m - 1

normal derivatives at each point of the surface S . To be specific , let us

that D ...

Oti ' . j = 0 éj , ig , - - - , é ; = 1 the coefficients ai . . . . it , . . . , in ) being

**assumed**tobe defined for t = [ ty , . ... having arbitrarily prescribed values and first m - 1

normal derivatives at each point of the surface S . To be specific , let us

**assume**that D ...

Page 1734

Since we have only to show that $ f is in H ( k + 1 / ( UI ) for some neighborhood U

ÇU , of p , it is clear that we may

70 = 1 , . This will be

Since we have only to show that $ f is in H ( k + 1 / ( UI ) for some neighborhood U

ÇU , of p , it is clear that we may

**assume**without loss of generality that U2 = U ,70 = 1 , . This will be

**assumed**in what follows . Making use of the properties ( i ) ...### 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