## Linear Operators: Spectral operators |

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Page 2137

Even though ( A ) is taken as a standing assumption throughout this section , it

will be indicated parenthetically in the statement of each

which it is used . 1

vectors in ...

Even though ( A ) is taken as a standing assumption throughout this section , it

will be indicated parenthetically in the statement of each

**lemma**in the proof ofwhich it is used . 1

**LEMMA**( A ) . If a , ß are complex numbers and x , y arevectors in ...

Page 2396

It follows from this formula just as in the proof of

following formula ( 14 ) ) that lim fu ( t ) = 0 , uniformly for ost < 0 . 141 - 00 дЄР +

Hence , by formula ( 24 ) of the proof of

It follows from this formula just as in the proof of

**Lemma**1 ( cf . the paragraphfollowing formula ( 14 ) ) that lim fu ( t ) = 0 , uniformly for ost < 0 . 141 - 00 дЄР +

Hence , by formula ( 24 ) of the proof of

**Lemma**3 , ĝu ( t ) ~ e - itu ; ģ ( t ) = - ime ...Page 2479

regarded as a subspace of the larger space H ' of

plainly H , may be regarded as the restriction to H , of the operator H of

15 ( cf . ( 33 ) – ( 36 ) above ) . Let Q be the projection of H ' onto its subspace Hı ,

and ...

regarded as a subspace of the larger space H ' of

**Lemma**15 , while equallyplainly H , may be regarded as the restriction to H , of the operator H of

**Lemma**15 ( cf . ( 33 ) – ( 36 ) above ) . Let Q be the projection of H ' onto its subspace Hı ,

and ...

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