## Linear Operators: Spectral theory |

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Page 972

From the preceding lemma it is seen that ( -xep ( 2 ) [ x , p ] 7- % e , for m , p in Mo

Xe 2 € R. Since characters have modulus

Plancherel's theorem that { u ( e + p ) } 2 = { u ( e ) } 2 . Hence if use ) < oo , we

have ...

From the preceding lemma it is seen that ( -xep ( 2 ) [ x , p ] 7- % e , for m , p in Mo

Xe 2 € R. Since characters have modulus

**equal**to unity , it follows fromPlancherel's theorem that { u ( e + p ) } 2 = { u ( e ) } 2 . Hence if use ) < oo , we

have ...

Page 1396

Then both deficiency indices of t are

extensions of To ( T ) have the same set of non - isolated points , and this set is

Theorem 5 and ...

Then both deficiency indices of t are

**equal**. Moreover , all the self adjointextensions of To ( T ) have the same set of non - isolated points , and this set is

**equal**to oe ( t ) . PROOF . The second assertion follows immediately fromTheorem 5 and ...

Page 1761

Let n be a function in Co ( -0 , +00 ) which is identically

and identically

Po - A ) ' f ) ( x ) ( 13 ) g ( x ; S ) = η ( s ) Σ XEC , 0 < sSx . j ! m j = 0 Then let g ( x ; 8

) ...

Let n be a function in Co ( -0 , +00 ) which is identically

**equal**to zero in ( -00 , 1 )and identically

**equal**to minus one in ( 1 , 0 ) . Let m = k ' +1 and let ( 8 — A ) ' ( (Po - A ) ' f ) ( x ) ( 13 ) g ( x ; S ) = η ( s ) Σ XEC , 0 < sSx . j ! m j = 0 Then let g ( x ; 8

) ...

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