## Linear Operators: Spectral theory |

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Page 1142

The validity of the

its validity in the range 2 Sp oo and from Lemma 9 . 14 . Q . E . D . In what follows

, we will use the symbols p and n to denote the continuous extension to the ...

The validity of the

**present**theorem in the range 1 < p S2 now follows at once fromits validity in the range 2 Sp oo and from Lemma 9 . 14 . Q . E . D . In what follows

, we will use the symbols p and n to denote the continuous extension to the ...

Page 1703

In the

partial differential operators to be defined below . A crucial theorem in the

development of the theory of Chapter XIII was Theorem XIII . 2 . 10 , which was

based on ...

In the

**present**section it will be seen that it can , at least for the class of ellipticpartial differential operators to be defined below . A crucial theorem in the

development of the theory of Chapter XIII was Theorem XIII . 2 . 10 , which was

based on ...

Page 1756

On the other hand , it follows from ( * * ) that VP = VP + 1 , so that , putting V = Vi ,

we have V in Ĉ ° ( E " + 1 ) , and the

consequence of ( ii ) . The remainder of the

that ( ii ) is ...

On the other hand , it follows from ( * * ) that VP = VP + 1 , so that , putting V = Vi ,

we have V in Ĉ ° ( E " + 1 ) , and the

**present**theorem is shown to be aconsequence of ( ii ) . The remainder of the

**present**proof is devoted to showingthat ( ii ) is ...

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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