## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 72

Page 1142

The validity of the

from its validity in the range 2 Sp Soo 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 s 2 now follows at oncefrom its validity in the range 2 Sp Soo 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 1679

Using ( 1 ) and ( 3 ) , we see that to establish the

show that ( 4 ) G ( S , ¥ ( * ) p ( • — y ) f ( y ) dy ) = S , G ( y ( • ) q ( • — y ) ) f ( y ) dy ,

where G = YF . Let K , be a compact subset of I containing in its interior a second

...

Using ( 1 ) and ( 3 ) , we see that to establish the

**present**lemma it suffices toshow that ( 4 ) G ( S , ¥ ( * ) p ( • — y ) f ( y ) dy ) = S , G ( y ( • ) q ( • — y ) ) f ( y ) dy ,

where G = YF . Let K , be a compact subset of I containing in its interior a second

...

Page 1756

On the other hand , it follows from ( * * ) that VP = VP + 1 , so that , putting V = V1 ,

we have V in Ĉ ° ( En + 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 = V1 ,

we have V in Ĉ ° ( En + 1 ) , and the

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

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

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

39 other sections not shown

### Other editions - View all

### 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 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 unit vanishes vector zero