## Linear Operators: Spectral theory |

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Results 1-3 of 83

Page 1112

Ann bu 1 Therefore , by Lagrange's expansion

matrix inverses , we have d det ( A + B ) 2 = 0 2 E bijli dz det ( A ) tr ( A 1B ) ,

where Vis denotes the cofactor of the element dis of the matrix A. Substituting A =

1 + ...

Ann bu 1 Therefore , by Lagrange's expansion

**formula**and Cramer's**formula**formatrix inverses , we have d det ( A + B ) 2 = 0 2 E bijli dz det ( A ) tr ( A 1B ) ,

where Vis denotes the cofactor of the element dis of the matrix A. Substituting A =

1 + ...

Page 1288

( Green's

order n on the finite closed interval I = [ a , b ] . If t , ge H ” ( I ) , then So ( 19 ) ( 0 ) (

t ) dt = S04 ( 1 ) ( ** g ) ( € ) de + F ( 1,8 ) –Felt , g ) . PROOF . In the discussion ...

( Green's

**formula**) Let T be a regular or irregular formal differential operator oforder n on the finite closed interval I = [ a , b ] . If t , ge H ” ( I ) , then So ( 19 ) ( 0 ) (

t ) dt = S04 ( 1 ) ( ** g ) ( € ) de + F ( 1,8 ) –Felt , g ) . PROOF . In the discussion ...

Page 1363

basis for this

projection in the resolution of the identity for T corresponding to ( 17 , ) may be

calculated from the resolvent by the

[ R ( 1 - ie ...

basis for this

**formula**is found in Theorem XII.2.10 which asserts that theprojection in the resolution of the identity for T corresponding to ( 17 , ) may be

calculated from the resolvent by the

**formula**1 80E + 0 + 2πι E ( ( 11 , ) ) } = lim lim[ R ( 1 - ie ...

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