## Linear Operators: Spectral operators |

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Page 2011

For every set o in E and every such matrix Â ( s ) we

8 ) , 8 + 0 , = 0 , so , and the operator Â , in HP ... In general , however , Âo need

not be bounded but it is always a closed and densely

For every set o in E and every such matrix Â ( s ) we

**define**the matrix Â ( 8 ) = 4 (8 ) , 8 + 0 , = 0 , so , and the operator Â , in HP ... In general , however , Âo need

not be bounded but it is always a closed and densely

**defined**operator . To see ...Page 2018

in the notation for the natural closed extension As , for in this case the symbol A is

used for the restriction As to O , that is , the formal differential operator which

...

in the notation for the natural closed extension As , for in this case the symbol A is

used for the restriction As to O , that is , the formal differential operator which

**defines**As . The spectra of the unbounded operators we have been discussing in...

Page 2284

As the measures Ma are finite , W , is

W12T , is a densely

inverse . We suppose the norm of [ h1 , . . . , hn ] in Hn is

14 ...

As the measures Ma are finite , W , is

**defined**and continuous , and the map An =W12T , is a densely

**defined**closed map of EmX into Hn with densely**defined**inverse . We suppose the norm of [ h1 , . . . , hn ] in Hn is

**defined**to be 11 / 2 ËS14 ...

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