## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1021

preceding remarks that the final conclusion of the lemma is equivalent to the

preceding remarks that the final conclusion of the lemma is equivalent to the

**statement**that | det ( A ) ( A - 1x , y ) = \ y ||| A || n - I ( n - 1 ) - ( n - 1 ) / 2 . Now , since W is unitary , det ( A ) = det ( W - 1 AW ) and ( A ...Page 1051

**Statement**( i ) is evident from Definition 1.**Statements**( ii ) and ( iii ) are evident consequences of Definition 1 and of the formulae En Sen g ( x ) dx = Sen ( Ux ) dx , 9 Sen clax ) dx = 121 - SemP ( ) dx , " which are valid for ...Page 1756

Hence we find that if \ y < r , f ( y ) = 0 , and

Hence we find that if \ y < r , f ( y ) = 0 , and

**statement**( i ) is fully proved . ( B ) The uniqueness of the function V of the theorem is an evident consequence of**statement**( i ) . Moreover ,**statement**( i ) enables us to reduce the ...### What people are saying - Write a review

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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero