## Linear Operators: Spectral theory |

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Page 1420

If A is considered as a subset of H , then the restriction of T ( 7 ' ) to A is a

continuous mapping of A into H. Then , assuming that t + t ' has a non -

leading coefficient , ( A ) the Hilbert spaces D ( T2 ( t + t ' ) ) and D ( T_ ( T ) ) have

the same ...

If A is considered as a subset of H , then the restriction of T ( 7 ' ) to A is a

continuous mapping of A into H. Then , assuming that t + t ' has a non -

**zero**leading coefficient , ( A ) the Hilbert spaces D ( T2 ( t + t ' ) ) and D ( T_ ( T ) ) have

the same ...

Page 1432

Suppose first that the end point under consideration is finite so that without loss of

generality we can suppose it to be at

by the leading coefficient a , of 1 , we can write the equation ( T - 2 ) } = 0 ) in the ...

Suppose first that the end point under consideration is finite so that without loss of

generality we can suppose it to be at

**zero**. Then , dividing through if necessaryby the leading coefficient a , of 1 , we can write the equation ( T - 2 ) } = 0 ) in the ...

Page 1727

... SL ( 6 ) = SLOm where L ' = [ li , ... , Im - 1 , m + 1 , In + 1 , ... , In ] and L = [ li , ... ,

in ] By ( 1 ) and by the definitions ( 2 ) , ( 3 ) , and ( 5 ) of Sı , it follows that ( 7 ) (

SL9 ) ( x ) = 0,9EC ( E " ) , -k Smin ( L ) < max ( L ) 3 k , if one of X1 , ... , xn is

... SL ( 6 ) = SLOm where L ' = [ li , ... , Im - 1 , m + 1 , In + 1 , ... , In ] and L = [ li , ... ,

in ] By ( 1 ) and by the definitions ( 2 ) , ( 3 ) , and ( 5 ) of Sı , it follows that ( 7 ) (

SL9 ) ( x ) = 0,9EC ( E " ) , -k Smin ( L ) < max ( L ) 3 k , if one of X1 , ... , xn is

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