Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 1247
If T is a positive self adjoint transformation , there is a unique positive self adjoint transformation A such that A2 = T. Proof . By Lemma 2 , o ( T ) C [ 0 , 0 ) and , by Theorem 2.6 ( d ) , the positive function f ( 2 ) = it on o ...
If T is a positive self adjoint transformation , there is a unique positive self adjoint transformation A such that A2 = T. Proof . By Lemma 2 , o ( T ) C [ 0 , 0 ) and , by Theorem 2.6 ( d ) , the positive function f ( 2 ) = it on o ...
Page 1250
Finally we show that the decomposition T = PA of the theorem is unique . ... Since A is unique , P is uniquely determined on R ( A ) by the equation of P ( Ar ) = Tr . Further the extension of P by continuity from R ( A ) to R ( A ) is ...
Finally we show that the decomposition T = PA of the theorem is unique . ... Since A is unique , P is uniquely determined on R ( A ) by the equation of P ( Ar ) = Tr . Further the extension of P by continuity from R ( A ) to R ( A ) is ...
Page 1383
With boundary conditions A and C , the unique solution of Tz0 = lo satisfying the boundary condition 130 = lo is sin vīt . With boundary conditions A , the eigenvalues are consequently to be determined from the equation sin vă = 0 .
With boundary conditions A and C , the unique solution of Tz0 = lo satisfying the boundary condition 130 = lo is sin vīt . With boundary conditions A , the eigenvalues are consequently to be determined from the equation sin vă = 0 .
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