## 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

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

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

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 .### What people are saying - Write a review

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