## Linear Operators: Spectral theory |

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Page 898

If we put E ( S ) = 0 when d n o T ) is void , then

from Theorem 1 and

defined spectral measure associated , in

is ...

If we put E ( S ) = 0 when d n o T ) is void , then

**Corollary**4 follows immediatelyfrom Theorem 1 and

**Corollary**IX.3.15 . Q.E.D. 5 DEFINITION . The uniquelydefined spectral measure associated , in

**Corollary**4 , with the normal operator Tis ...

Page 1142

Q.E.D. In what follows , we will use the symbols p and n to denote the continuous

extension to the classes C , of operators of the mappings p and n of the previous

lemma . We will also write t = ( p + n ) / 2 . We note the following

Q.E.D. In what follows , we will use the symbols p and n to denote the continuous

extension to the classes C , of operators of the mappings p and n of the previous

lemma . We will also write t = ( p + n ) / 2 . We note the following

**corollary**.Page 1301

However , as vo satisfies an equation of order 2n , v , must be identically zero .

This contradiction completes the proof . Q.E.D. 23

formal differential operator of order n on an interval I with end points a , b , and

suppose ...

However , as vo satisfies an equation of order 2n , v , must be identically zero .

This contradiction completes the proof . Q.E.D. 23

**COROLLARY**. Let t be aformal differential operator of order n on an interval I with end points a , b , and

suppose ...

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

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