Linear Operators: Spectral theory |
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Page 890
... projections E ( 2 : ) for which died , then the function E is a resolution of the
identity for T and the operational calculus is given by the formula ( vi ) ( T ) = Som
f ( 2 ) E ( da ) , where the integral is defined as the finite sum Ik - 1 / ( 2 ; ) E ( 7 : ) .
... projections E ( 2 : ) for which died , then the function E is a resolution of the
identity for T and the operational calculus is given by the formula ( vi ) ( T ) = Som
f ( 2 ) E ( da ) , where the integral is defined as the finite sum Ik - 1 / ( 2 ; ) E ( 7 : ) .
Page 1089
The characteristic numbers un ( T ) of a compact operator are given by the
following formula : Mn + 1 ( T ) = min max 6Tol , n20 . 10 = 1 ( 9 , 91 ) = . . . = ( 0 , 9
) = 0 Proof . This formula may be written ( un ( T ) ) 2 = min max To | 2 . P1 , . . . ,
Pm 10 ...
The characteristic numbers un ( T ) of a compact operator are given by the
following formula : Mn + 1 ( T ) = min max 6Tol , n20 . 10 = 1 ( 9 , 91 ) = . . . = ( 0 , 9
) = 0 Proof . This formula may be written ( un ( T ) ) 2 = min max To | 2 . P1 , . . . ,
Pm 10 ...
Page 1363
basis for this formula is found in Theorem XII . 2 . 10 which asserts that the
projection in the resolution of the identity for T corresponding to ( 17 , 12 ) may be
calculated from the resolvent by the formula 1 po - 8 E ( ( , 22 ) ) = - lim lim ( R ( 2
— ię ...
basis for this formula is found in Theorem XII . 2 . 10 which asserts that the
projection in the resolution of the identity for T corresponding to ( 17 , 12 ) may be
calculated from the resolvent by the formula 1 po - 8 E ( ( , 22 ) ) = - lim lim ( R ( 2
— ię ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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