## Linear Operators: Spectral operators |

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Page 2063

... S is the one point compactification of N - dimensional Euclidean space RN and

e is the self adjoint spectral measure given in equation ( 11 . 15 ) . We know from

Lemma 9 . 2 that if the elements a , A in A , AP ,

... S is the one point compactification of N - dimensional Euclidean space RN and

e is the self adjoint spectral measure given in equation ( 11 . 15 ) . We know from

Lemma 9 . 2 that if the elements a , A in A , AP ,

**respectively**, possess bounded ...Page 2108

Let u (

in order for there to exist a necessarily unique spectral measure d on the Baire

sets in X X Y to A such that ( 8 x 0 ) = u ( d ) v ( o ) for all d , o , it is necessary and

...

Let u (

**respectively**, v ) be a spectral measure on X (**respectively**, Y ) to A . Thenin order for there to exist a necessarily unique spectral measure d on the Baire

sets in X X Y to A such that ( 8 x 0 ) = u ( d ) v ( o ) for all d , o , it is necessary and

...

Page 2109

Then the mappings u → ( d / dt ) ( pdu / dt ) + qu on CO ( Tl ) and D ( T1 ) are

scalar . ( c ) The mappings u → - d u / dta + t u on the spaces Ø (

of rapidly decreasing CR functions (

...

Then the mappings u → ( d / dt ) ( pdu / dt ) + qu on CO ( Tl ) and D ( T1 ) are

scalar . ( c ) The mappings u → - d u / dta + t u on the spaces Ø (

**respectively**, Tl )of rapidly decreasing CR functions (

**respectively**, tempered distributions ) on the...

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