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

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Page 1223

How are we to choose its

How are we to choose its

**domain**? A natural first guess is to choose as**domain**the collection D , of all functions with one continuous derivative . If f and g are any two such functions , we have ( iDf , g ) = Sit ' ( 1 ) 8 ( t ) dt ...Page 1249

Thus PP * is a projection whose range is N = PM , the final

Thus PP * is a projection whose range is N = PM , the final

**domain**of P. To complete the proof it will suffice to show that P * P is a projection if P is a partial isometry . Let x , v E M , the initial**domain**of P. Then the identity ...Page 1669

Let I be a

Let I be a

**domain**in E " !, and let 1 , be a ,**domain**in E " ?. Let M : 11 +1 , be a mapping of l , into 1 , such that ( a ) M - 1C is a compact subset of I , whenever C is a compact subset of I , ; ( b ) ( M ( - ) ) , e Co ( 11 ) ...### 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