## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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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 1 ( 8 X 0 ) = u ( d ) v ( o ) for all 8 , o , it is necessary ...

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 1 ( 8 X 0 ) = u ( d ) v ( o ) for all 8 , o , it is necessary ...

Page 2109

( c ) The mappings u → - d u / dta + tzu on the spaces 0 (

rapidly decreasing Co functions (

real line are scalar . Thus the Fourier transform u ( t ) → SR e - 2a itsu ( s ) ds ...

( c ) The mappings u → - d u / dta + tzu on the spaces 0 (

**respectively**, Tl ) ofrapidly decreasing Co functions (

**respectively**, tempered distributions ) on thereal line are scalar . Thus the Fourier transform u ( t ) → SR e - 2a itsu ( s ) ds ...

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