## Linear Operators: Spectral operators |

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Page 1930

If Eis a Boolean algebra of subsets of the complex

set and the whole

spectral measure E on is called a resolution of the identity ( or a spectral ...

If Eis a Boolean algebra of subsets of the complex

**plane**which contains the voidset and the whole

**plane**, in short , if is a field of sets in the complex**plane**, then aspectral measure E on is called a resolution of the identity ( or a spectral ...

Page 2087

... ( p ) T ( 29 ) ( RN ) is the infinitesimal generator of a strongly continuous semi -

group S ( t ) , t 20 , of bounded linear operators in HP and S ( t ) has a strongly

analytic extension to a semi - group $ ( $ ) defined for & in the half

0 .

... ( p ) T ( 29 ) ( RN ) is the infinitesimal generator of a strongly continuous semi -

group S ( t ) , t 20 , of bounded linear operators in HP and S ( t ) has a strongly

analytic extension to a semi - group $ ( $ ) defined for & in the half

**plane**R ( $ ) >0 .

Page 2335

If I is in the right half -

lies in the angular sector { u | 77 / 2n 2 argu > - / 2n } . If , is in the left half -

let ula ) denote that unique nth root of which lies in the angular sector { u . 77 / 2n

...

If I is in the right half -

**plane**, let u = u ( a ) denote that unique nth root of whichlies in the angular sector { u | 77 / 2n 2 argu > - / 2n } . If , is in the left half -

**plane**,let ula ) denote that unique nth root of which lies in the angular sector { u . 77 / 2n

...

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